A009360 Expansion of e.g.f. log(1+sinh(x)*x) (even powers only).

0, 2, -8, 126, -4248, 246250, -21819060, 2741961054, -463859694704, 101639490015186, -28002426109496940, 9474407274253732294, -3861976880978567739432, 1866672045348038810596026

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..229

Crossrefs

Cf. A133866.

Programs

Maple

S:= series(log(1+sinh(x)*x),x,61):
seq(k!*coeff(S,x,k),k=0..60,2); # Robert Israel, Jan 04 2019

Mathematica

Log[ 1+Sinh[ x ]*x ] (* Even Part *)

Formula

From Robert Israel, Jan 04 2019: (Start)

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

a(n) ~ (-1)^(n+1)*(2*n)!/(n*r^(2*n)) where r is the zero of x*sin(x)-1 near 1.114157 (see A133866). (End)

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997