A009541 Expansion of sin(x)*exp(sin(x)).

0, 1, 2, 2, -4, -24, -42, 104, 888, 1792, -8086, -68608, -115468, 1203840, 8863806, 5570816, -275344656, -1636425728, 2488177106, 86205304832, 369676840940, -2289265803264, -34139482063962, -73881736609792, 1691837365047912

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Crossrefs

A009623.

Programs

Mathematica

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

Maxima

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 */

Formula

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

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Dec 09 2021