A009209 Expansion of e.g.f.: exp(sin(x))/exp(x).

1, 0, 0, -1, 0, 1, 10, -1, -56, -279, 246, 4619, 14388, -53195, -556478, -864865, 13276912, 90192753, -72903378, -3987888493, -16957067028, 101506932205, 1411655530330, 2206092853799, -70455418153496, -549095655588183, 1428569363164230

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Crossrefs

Cf. A002017, A009227.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Sin[x]]/Exp[x],{x,0,nn}], x]Range[0,nn]!] (* Harvey P. Dale, Jun 27 2012 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(sin(x))/exp(x))) \\ Michel Marcus, Apr 09 2022

Formula

a(0) = 1; a(n) = Sum_{k=1..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1). - Ilya Gutkovskiy, Apr 09 2022

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, Jun 27 2012