A009541 - OEIS

%I #21 Dec 09 2021 18:58:44

%S 0,1,2,2,-4,-24,-42,104,888,1792,-8086,-68608,-115468,1203840,8863806,

%T 5570816,-275344656,-1636425728,2488177106,86205304832,369676840940,

%U -2289265803264,-34139482063962,-73881736609792,1691837365047912

%N Expansion of sin(x)*exp(sin(x)).

%F a(n)=sum(k=1..n, (1+(-1)^(n-k))*2^(-k)*sum(i=0..k/2, (-1)^((n+k)/2-i)*binomial(k,i)*(2*i-k)^n)/(k-1)!). - _Vladimir Kruchinin_, Apr 19 2011

%F a(n) = D^n(x*exp(x)) evaluated at x = 0, where D is the operator sqrt(1-x^2)*d/dx. Cf. A009623. - _Peter Bala_, Dec 06 2011

%t With[{nn=30},CoefficientList[Series[Sin[x]*Exp[Sin[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 09 2021 *)

%o (Maxima)

%o a(n):=sum((1+(-1)^(n-k))*2^(-k)*sum((-1)^((n+k)/2-i)*binomial(k,i)*(2*i-k)^n,i,0,k/2)/(k-1)!,k,1,n); /* _Vladimir Kruchinin_, Apr 19 2011 */

%Y A009623.

%K sign,easy

%O 0,3

%A _R. H. Hardin_

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

%E Previous Mathematica program replaced by _Harvey P. Dale_, Dec 09 2021