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

0,3

Links

Table of n, a(n) for n=0..24.

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

Mathematica

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

Prog

(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 */

Crossrefs

A009623.

Sequence in context: A270527 A232275 A257612 * A307969 A212672 A362766

Adjacent sequences: A009538 A009539 A009540 * A009542 A009543 A009544

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

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

Status

approved