A009403 Expansion of e.g.f. log(1 + tanh(x)^2), even powers only.

0, 2, -28, 992, -69088, 8110592, -1448424448, 366436769792, -124760831684608, 55014520738414592, -30501848618302701568, 20768078187214502100992, -17035983844637174375907328, 16570619538920401323784404992

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

Cf. A024299.

Sequence in context: A352251 A012756 A362587 * A026944 A296464 A292806

Adjacent sequences: A009400 A009401 A009402 * A009404 A009405 A009406

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Aug 27 2013

Status

approved