OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
FORMULA
a(n) ~ (-1)^(n+1) * 2^(4*n) * (2*n)! / (n * Pi^(2*n)). - Vaclav Kotesovec, Apr 20 2014
From G. C. Greubel, Jul 12 2022: (Start)
a(n) = 2*A024299(n).
a(n) = -4^n * (4^n - 2)*(4^n - 1)*Zeta(1-2*n), with a(0) = 0. (End)
MATHEMATICA
With[{nn=30}, Take[CoefficientList[Series[Log[1+Tanh[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Aug 27 2013 *)
PROG
(Magma)
L:=RiemannZeta();
[0] cat [-Round(4^n*(4^n-2)*(4^n-1)*Evaluate(L, 1-2*n)): n in [1..20]]; // G. C. Greubel, Jul 12 2022
(SageMath) [0]+[-4^n*(4^n-2)*(4^n-1)*zeta(1-2*n) for n in (1..20)] # G. C. Greubel, Jul 12 2022
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Previous Mathematica program replaced by Harvey P. Dale, Aug 27 2013
STATUS
approved