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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/2586.txt b/2586.txt new file mode 100644 index 0000000..19b016e --- /dev/null +++ b/2586.txt @@ -0,0 +1,1966 @@ +*The Project Gutenberg Etext of The first 498 Bernoulli Numbers* +#22 in our series of math constants + + +Copyright laws are changing all over the world, be sure to check +the copyright laws for your country before posting these files!! + +Please take a look at the important information in this header. +We encourage you to keep this file on your own disk, keeping an +electronic path open for the next readers. Do not remove this. + + +**Welcome To The World of Free Plain Vanilla Electronic Texts** + +**Etexts Readable By Both Humans and By Computers, Since 1971** + +*These Etexts Prepared By Hundreds of Volunteers and Donations* + +Information on contacting Project Gutenberg to get Etexts, and +further information is included below. We need your donations. + + +Title: The first 498 Bernoulli Numbers + +Editor: Simon Plouffe + +April, 2001 [Etext #2586] + + +*The Project Gutenberg Etext of The first 498 Bernoulli Numbers* +******This file should be named 2586.txt or 2586.zip****** + + +Mathematical constants and numbers +edited by +Simon Plouffe +Associate Professor +LaCIM, University of Quebec at Montreal +http://www.lacim.uqam.ca/pi : Plouffe's Inverter +plouffe@math.uqam.ca + +Project Gutenberg Etexts are usually created from multiple editions, +all of which are in the Public Domain in the United States, unless a +copyright notice is included. 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FOR PUBLIC DOMAIN ETEXTS*Ver.04.29.93*END* + + + + + +Mathematical constants and numbers +edited by +Simon Plouffe +Associate Professor +LaCIM, University of Quebec at Montreal +http://www.lacim.uqam.ca/pi : Plouffe's Inverter +plouffe@math.uqam.ca + + + + + +The first 498 Bernoulli numbers are the coefficients +of the series expansion of + +t*exp(x*t)/(exp(t)-1) = sum( B(n,x)/n!*t^n, n=0..infinity ). + + +Bernoulli(2) +1/6 + +Bernoulli(4) +-1/30 + +Bernoulli(6) +1/42 + +Bernoulli(8) +-1/30 + +Bernoulli(10) +5/66 + +Bernoulli(12) +-691/2730 + +Bernoulli(14) +7/6 + +Bernoulli(16) +-3617/510 + +Bernoulli(18) +43867/798 + +Bernoulli(20) +-174611/330 + +Bernoulli(22) +854513/138 + +Bernoulli(24) +-236364091/2730 + +Bernoulli(26) +8553103/6 + +Bernoulli(28) +-23749461029/870 + +Bernoulli(30) +8615841276005/14322 + +Bernoulli(32) +-7709321041217/510 + +Bernoulli(34) +2577687858367/6 + +Bernoulli(36) +-26315271553053477373/1919190 + +Bernoulli(38) +2929993913841559/6 + +Bernoulli(40) +-261082718496449122051/13530 + +Bernoulli(42) +1520097643918070802691/1806 + +Bernoulli(44) +-27833269579301024235023/690 + +Bernoulli(46) +596451111593912163277961/282 + +Bernoulli(48) +-5609403368997817686249127547/46410 + +Bernoulli(50) +495057205241079648212477525/66 + +Bernoulli(52) +-801165718135489957347924991853/1590 + +Bernoulli(54) +29149963634884862421418123812691/798 + +Bernoulli(56) +-2479392929313226753685415739663229/870 + +Bernoulli(58) +84483613348880041862046775994036021/354 + +Bernoulli(60) +-1215233140483755572040304994079820246041491/56786730 + +Bernoulli(62) +12300585434086858541953039857403386151/6 + +Bernoulli(64) +-106783830147866529886385444979142647942017/510 + +Bernoulli(66) +1472600022126335654051619428551932342241899101/64722 + +Bernoulli(68) +-78773130858718728141909149208474606244347001/30 + +Bernoulli(70) +1505381347333367003803076567377857208511438160235/4686 + +Bernoulli(72) +-5827954961669944110438277244641067365282488301844260429/140100870 + +Bernoulli(74) +34152417289221168014330073731472635186688307783087/6 + +Bernoulli(76) +-24655088825935372707687196040585199904365267828865801/30 + +Bernoulli(78) +414846365575400828295179035549542073492199375372400483487/3318 + +Bernoulli(80) +-4603784299479457646935574969019046849794257872751288919656867/230010 + +Bernoulli(82) +1677014149185145836823154509786269900207736027570253414881613/498 + +Bernoulli(84) +-2024576195935290360231131160111731009989917391198090877281083932477/3404310 + +Bernoulli(86) +660714619417678653573847847426261496277830686653388931761996983/6 + +Bernoulli(88) +-1311426488674017507995511424019311843345750275572028644296919890574047/61410 + +Bernoulli(90) +1179057279021082799884123351249215083775254949669647116231545215727922535/ +272118 + +Bernoulli(92) +-1295585948207537527989427828538576749659341483719435143023316326829946247/1410 + +Bernoulli(94) +1220813806579744469607301679413201203958508415202696621436215105284649447/6 + +Bernoulli(96) +-211600449597266513097597728109824233673043954389060234150638733420050668349987 +259/4501770 + +Bernoulli(98) +67908260672905495624051117546403605607342195728504487509073961249992947058239/6 + +Bernoulli(100) +-945980378191221252952274330694937218727028415330669361333856962043113954151972 +47711/33330 + +Bernoulli(102) +3204019410860907078243020782116241775491817197152717450679002501086861530836678 +158791/4326 + +Bernoulli(104) +-319533631363830011287103352796174274671189606078272738327103470162849568365549 +721224053/1590 + +Bernoulli(106) +3637390317261741440815182015159342716923129864058169003893081637828187987338620 +2346572901/642 + +Bernoulli(108) +-346934224784782878955208865932385254139976678576049114687000589137150126631972 +4897592306597338057/209191710 + +Bernoulli(110) +7645992940484742892248134246724347500528752413412307906683593870759797606269585 +779977930217515/1518 + +Bernoulli(112) +-265087960215509971335259721468516201444315149919250989645178842768096675651487 +5515366781203552600109/1671270 + +Bernoulli(114) +2173783231936916333331076108665299147572115667909083136080611011493360548423459 +3650904188618562649/42 + +Bernoulli(116) +-309553916571842976912513458033841416869004128064329844245504045721008957524571 +968271388199595754752259/1770 + +Bernoulli(118) +3669631199697131115349471515855850066846063610806992043010594406764144850458064 +61889371776354517095799/6 + +Bernoulli(120) +-515074865350791090618439968578499832740951703532626752130928691671992974749229 +85358811329367077682677803282070131/2328255930 + +Bernoulli(122) +4963366607926258191253263747599075743872279031106013977030931179315068321410043 +1329033113678098037968564431/6 + +Bernoulli(124) +-958767753342471287507749031075424446205788300132973368195535127293585933544359 +44413631943610268472689094609001/30 + +Bernoulli(126) +5556330281949274850616324408918951380525567307126747246796782304333594286400508 +981287241419934529638692081513802696639/4357878 + +Bernoulli(128) +-267754707742548082886954405585282394779291459592551740629978686063357792734863 +530145362663093519862048495908453718017/510 + +Bernoulli(130) +1928215175136130915645299522271596435307611010164728458783733020528548622403504 +078595174411693893882739334735142562418015/8646 + +Bernoulli(132) +-410951945846993378209020486523571938123258077870477502433469747962650070754704 +863812646392801863686694106805747335370312946831/4206930 + +Bernoulli(134) +2645901718707177256336357372488790151512545255931686884119185548406677655916905 +40727987316391252434348664694639349484190167/6 + +Bernoulli(136) +-842902263433674051312875780603661936493366123975474357671892069122304422426282 +12786558235455817749737691517685781164837036649737/4110 + +Bernoulli(138) +2694866548990880936043851683724113040849078494664282483862150893060478501559546 +243423633375693325757795709438325907154973590288136429/274386 + +Bernoulli(140) +-328949098643589880393069954885188400688053747693113098130746708516250480297361 +8096693859598125274741604181467826651144393874696601946049/679470 + +Bernoulli(142) +1473185328088858956587008044245321423980421702399064267619487899740754606158164 +3106569966189211748270209483494554402556608073385149191/6 + +Bernoulli(144) +-305024469837360756503515583690172635740500710425656676188419185243485103374476 +1276392695669329626855965183503295793517411526056244431024612640493/2381714790 + +Bernoulli(146) +4120570026280114871526113315907864026165545608808541153973817680034790262683524 +284855810008621905238290240143481403022987037271683989824863/6 + +Bernoulli(148) +-169173714561401897986556109511216618960768285214730140081648067591695787117864 +8433284821493606361235973346584667336181793937950344828557898347149/4470 + +Bernoulli(150) +4633655793891627414432844258118062649822337254252957998522998073253793155015723 +05760030594769688296308375193913787703707693010224101613904227979066275/2162622 + +Bernoulli(152) +-373701814115510850210589288849128216583748953148893295176850712718240973132847 +2084456653639812530140212355374618917309552824925858430886313795805601/30 + +Bernoulli(154) +1025971868203802105102779423837918446102573865246056923399277648975088133750686 +3808448685054322627708245455888249006715516690124228801409697850408284121/138 + +Bernoulli(156) +-817180860832626285107564597536734523135957103961164675821520905960925486991383 +4694299550948828465080397683633716467049473386655982976884836350662433481896141 +9869/1794590070 + +Bernoulli(158) +1716726769011532100721830835061033951375139222740295641505001352653081481973585 +51999205867870374013289728260984269623579880772408522396975250682773558018919/6 + +Bernoulli(160) +-424086079420331037606556349236115694998939808708637321471062577845844194047783 +9981850928830420029285687066701804645453159767402961229305942765784122421197736 +180867/230010 + +Bernoulli(162) +1584451495144416428390934243279426140836596476080786316960222380784239380974799 +8803643636479781686345904182158544197937165493888659053485343756299287320087862 +33507729/130074 + +Bernoulli(164) +-205380646091432162655719795866926468378053310231486450681333723839303449483166 +0059120392638854094081483317332279380432508494509482852486062609201354728133535 +6200073083/2490 + +Bernoulli(166) +5734032969370860921631095311392645731505222358555208498573088911303001784652122 +9647032057527091941930952463086112641216788342507044680826483137881247541686718 +15815821441/1002 + +Bernoulli(168) +-138448285151763960812383465850635172285311091569843452492604539343177727548367 +9125898751654032498361156975864952598334740858904573417658927014305850902639224 +6407576578281097477/3404310 + +Bernoulli(170) +1953342076266375304149767792384622344814103373509884272151399957073469791246869 +1826768817153635265057253533036981817697995193147742759487278301874989469915791 +7782460035894085/66 + 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+jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..974506d --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #2586 (https://www.gutenberg.org/ebooks/2586) |