A009334 E.g.f. log(1+sin(x))*exp(x).

0, 1, 1, 1, 0, 0, -5, 5, -56, 224, -1441, 9029, -64592, 497068, -4153357, 37288173, -358469008, 3672613632, -39954165153, 459970973037, -5587015067704, 71405586701516, -957909748415229, 13458304798985221, -197627582943979080

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• Matthew House, Table of n, a(n) for n = 0..486

Crossrefs

Cf. A000111.

Programs

Maple

S:= series(log(1+sin(x))*exp(x), x, 101):
seq(coeff(S,x,j)*j!,j=0..100); # Robert Israel, Aug 06 2015

Mathematica

CoefficientList[Series[E^x*Log[1 + Sin[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

Formula

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

a(n) = Sum_{j=0..n-1}(-1)^j*binomial(n,j+1)*A000111(j). - Robert Israel, Aug 06 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997