A009206 Expansion of e.g.f.: exp(sin(x))*x.

0, 1, 2, 3, 0, -15, -48, -21, 448, 1953, 640, -32461, -152064, 77649, 4331264, 18557595, -46686208, -894805183, -2948087808, 21405607651, 254321049600, 421226202033, -10904188190720, -90171090228021, 96102216892416, 6418365899545825

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Sin[x]]*x,{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Dec 25 2021 *)

Formula

a(n) = n * A002017(n-1). - Ralf Stephan, Sep 01 2003

E.g.f.: x*E(0) -x, where E(k) = 2 + sin(x)/(2*k+1 - sin(x)/E(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 24 2013

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Dec 25 2021