A009282 Expansion of e.g.f.: exp(x + sin(x)).

1, 2, 4, 7, 8, -7, -74, -209, -40, 2441, 10954, 6667, -185524, -1041739, -510530, 26716831, 158378768, -47260303, -6226501934, -34323431789, 71521515284, 2087815263725, 9437342779558, -55046954388953, -923175950185960, -2736047549718871, 43387645616657338

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Crossrefs

Cf. A002017, A009209, A009283.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x+Sin[x]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Aug 23 2014 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(x + sin(x)))) /* Joerg Arndt, Sep 01 2012 */

Formula

E.g.f.: exp(x + sin(x)).

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1). - Ilya Gutkovskiy, Apr 10 2022

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Name corrected by Arkadiusz Wesolowski, Sep 01 2012