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Search: id:A129826
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| A129826 |
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Transformed Bernoulli twin numbers. |
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+0
10
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| 1, -1, -2, -4, -4, 24, 120, -960, -12096, 120960, 3024000, -36288000, -1576143360, 22066007040, 1525620096000, -24409921536000, -2522591034163200, 45406638614937600, 6686974460694528000, -133739489213890560000, -27033456071346536448000, 594736033569623801856000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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We define Bernoulli twin numbers C(n) via Bernoulli numbers B(n)=A027641(n)/A027642(n) as C(0)=1, 2C(1)=-1, 3C(2)=-1, C(2n-1)= -B(2n-2) and C(2n)=B(2n), n>1. The sequence is defined as a(n)=(n+1)!*C(n).
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FORMULA
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C(n) = A051718(n)/A051717(n).
E.g.f.: Sum(n>=0)C(n) x^n/n! = 1 + x - x^2/2 + sum_{n>=1}[B(n)-B(n-1)]x^n/n! = x - x^2/2 + x/(e^x-1) - integral_{y=0..x}((y dy)/(e^y-1)).
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EXAMPLE
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C(0)=1; C(1)= -1/2; C(2)= -1/3; C(3)= -1/6; C(4)= -1/30; C(5)=1/30.
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CROSSREFS
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Cf. A129378, A140351.
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KEYWORD
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sign,new
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 20 2007
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 06 2008
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