A009206 - OEIS

%I #22 Dec 25 2021 12:05:39

%S 0,1,2,3,0,-15,-48,-21,448,1953,640,-32461,-152064,77649,4331264,

%T 18557595,-46686208,-894805183,-2948087808,21405607651,254321049600,

%U 421226202033,-10904188190720,-90171090228021,96102216892416,6418365899545825

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

%F a(n) = n * A002017(n-1). - _Ralf Stephan_, Sep 01 2003

%F 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

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

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Dec 25 2021