A009337 Expansion of e.g.f.: log(1+sin(x))/exp(x).

0, 1, -3, 7, -16, 40, -117, 411, -1720, 8384, -46561, 289595, -1991504, 14993108, -122595085, 1081616659, -10239597968, 103522029312, -1113074512289, 12681693805203, -152613117638712, 1934275341388596, -25753344727083773

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Comments

This sequence starting with the 2nd term, unsigned, is the partial sums of A000667. - Gerald McGarvey, Aug 13 2004

Crossrefs

Cf. A000667.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Log[1+Sin[x]]/Exp[x],{x,0,nn}], x] Range[0,nn]!] (* Harvey P. Dale, Aug 13 2012 *)

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * exp(Pi/2) * 2^(n+1) / Pi^n. - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, Aug 13 2012