A009360 - OEIS

%I #19 Jan 05 2019 06:56:33

%S 0,2,-8,126,-4248,246250,-21819060,2741961054,-463859694704,

%T 101639490015186,-28002426109496940,9474407274253732294,

%U -3861976880978567739432,1866672045348038810596026

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

%H Robert Israel, <a href="/A009360/b009360.txt">Table of n, a(n) for n = 0..229</a>

%F From _Robert Israel_, Jan 04 2019: (Start)

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

%F 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)

%p S:= series(log(1+sinh(x)*x),x,61):

%p seq(k!*coeff(S,x,k),k=0..60,2); # _Robert Israel_, Jan 04 2019

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

%Y Cf. A133866.

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997