The Genocchi numbers G(n): (the non-zero ones) Sum_{n>=1} G(n) t^n/n! = 2t / (exp(t) + 1) The realation to the Bernoulli numbers: B(2m) = G(2m) / ( 2 * (1 - 2^(2m)) ) Reference: Comtet p 49 ---------------------------------------------------------------------------- ANNOUNCEMENT of: CALCULATION OF THE 10000'th Bernoulli Number by Greg J. Fee and Simon Plouffe Centre for Experimental & Constructive Mathematics June 20, 1996 We just completed the calculation of the 10000'th Bernoulli number on a SiliconGraphics R4000 computer. We ask here if somebody can do better... We denote the n'th bernoulli number by B(n) and the first few are: B(0)=1, B(1)=-1/2, B(2)=1/6, B(3)=0, B(4)=-1/30, ... B(10000) is approximately -0.904942396360948*10^27678 . When B(10000) is written as a rational number, then the numerator has 27691 digits and the denominator has 13 digits. I used to circulate a screen hardcopy with a picture of Zippy the Pinhead saying, "YOW, I divided my NASDAQ ticker by Lee Trevino's lifetime golf score, and accidentally computed the 10000th Bernoulli number!" That gray fuzz covering most of the page really was the 10000th Bernoulli number. I once included a copy in a letter to F. J. Dyson, and he wrote back to say "My eye fell immediately upon the six consecutive 5's. ..." I wrote him back asking for the name of his opthalmologist. (c2176) load("sh:>rwg>climax>b10000")$ SWEATHOUSE:>rwg>climax>b10000.lisp.1 being loaded. (c2177) b10000; (d2177) - 21159583804629094072179273804098908566542935798860836879253005 757496397746134765980606098841266504937826320601# 522888495150776738178803088207279567024298155971140153644163393860274678 89772264916572127220444818117/2338224387510 (c2178) bfloat(%); (d2178) - 9.04942396360948050052924144308354b27677 Developmental feature: (c2179) bern(10002.b0); Time= 21318 msecs (d2179) 2.29293358779099388987640825261525b27684