A024286 Expansion of e.g.f. log(1+sin(x)*x)/2 (even coefficients).

0, 1, -8, 183, -8852, 733685, -92907942, 16685025455, -4033626509768, 1263031247390697, -497267081169369290, 240429918597334607075, -140051748469197955343340, 96736260363763053291403613, -78176444639905678751886122222, 73077125090731363505146141810455

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..85

Crossrefs

Cf. A009341.

Programs

Maple

a:= n-> coeff(series(ln(1+sin(x)*x)/2,x,2*n+1),x,2*n)*(2*n)!:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 03 2012

Mathematica

Log[ 1+Sin[ x ]*x ]/2 (* Even Part *)

Formula

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

Extensions

Extended with signs Mar 1997