A024299 a(n) = (2*n)! [x^(2*n)] log(1 + tanh(x)^2)/2.

0, 1, -14, 496, -34544, 4055296, -724212224, 183218384896, -62380415842304, 27507260369207296, -15250924309151350784, 10384039093607251050496, -8517991922318587187953664, 8285309769460200661892202496, -9429010285390912531529354706944

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..215

Crossrefs

Cf. A009403.

Cf. A003707, A101921.

Programs

Magma

L:=RiemannZeta();
[0] cat [-Round(2^(2*n-1)*(4^n-2)*(4^n-1)*Evaluate(L, 1-2*n)): n in [1..15]]; // G. C. Greubel, Jul 12 2022

Maple

a := n -> `if`(n=0, 0, -2^(2*n-1)*(4^n-2)*(4^n-1)*Zeta(1-2*n)):
seq(a(n), n=0..14); # Peter Luschny, Oct 29 2020

Mathematica

With[{nn=30},Take[CoefficientList[Series[Log[1+Tanh[x]^2]/2,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Dec 12 2021 *)

PARI

my(x='x+O('x^30), v = concat([0,0], Vec(serlaplace (log(1+tanh(x)^2)/2)))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Oct 29 2020

SageMath

[0]+[-2^(2*n-1)*(4^n-2)*(4^n-1)*zeta(1-2*n) for n in (1..15)] # G. C. Greubel, Jul 12 2022

Formula

a(n) = A009403(n)/2.

a(n) = -2^(2*n-1)*(4^n - 2)*(4^n - 1)*zeta(1-2*n) for n >= 1. - Peter Luschny, Oct 29 2020

Extensions

Extended with signs, Mar 1997

Previous Mathematica program replaced by Harvey P. Dale, Dec 12 2021