A009483 - OEIS

%I #16 Apr 01 2017 14:29:59

%S 0,1,2,1,-12,-83,-338,-555,4872,58713,355322,988073,-6857796,

%T -129165307,-1078218906,-4414644611,23381079184,664338643633,

%U 7109036257394,38790001170257,-152532610916348,-6632928177660835,-87579228437764450

%N E.g.f. sin(sin(x)*exp(x)).

%F a(n)=sum(j=0..(n-1)/2, (2^(-(2*j))*sum(k=j..(n-1)/2, binomial(n,n-2*k-1)*((2*j+1)^(n-2*k-1)*sum(i=0..(2*j+1)/2, (2*i-2*j-1)^(2*k+1)*binomial(2*j+1,i)*(-1)^(k+1-i)))))/(2*j+1)!). - _Vladimir Kruchinin_, Jun 13 2011

%t With[{nn=30},CoefficientList[Series[Sin[Sin[x]Exp[x]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Jun 12 2013 *)

%o (Maxima)

%o a(n):=sum((2^(-(2*j))*sum(binomial(n,n-2*k-1)*((2*j+1)^(n-2*k-1)*sum((2*i-2*j-1)^(2*k+1)*binomial(2*j+1,i)*(-1)^(k+1-i),i,0,(2*j+1)/2)),k,j,(n-1)/2))/(2*j+1)!,j,0,(n-1)/2); /* _Vladimir Kruchinin_, Jun 13 2011 */

%K sign,easy

%O 0,3

%A _R. H. Hardin_

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