A007118 Expansion of e.g.f. (1+x)^sin(x). (Formerly M0916)

1, 0, 2, -3, 16, -80, 440, -3171, 24680, -218952, 2170018, -23566675, 279907076, -3603250716, 49968204078, -742893013695, 11785962447792, -198748512229968, 3550002639307890, -66954457199954115, 1329661510693923636

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = sum(k=1..n, sum(r=0..n/2-k, binomial(n,2*r+k)*(stirling1(n-2*r-k,k)*sum(i=0..k/2, (2*i-k)^(2*r+k)*binomial(k,i)*(-1)^(r+k-i))))/2^(k-1)), n>0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011

|a(n)| ~ n! * n^(sin(1)-1)/Gamma(sin(1)). - Vaclav Kotesovec, Jun 27 2013

Mathematica

With[{nn=30}, CoefficientList[Series[(1+x)^Sin[x], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jan 20 2013 *)

Prog

(Maxima)
a(n):=sum(sum(binomial(n, 2*r+k)*(stirling1(n-2*r-k, k)*sum((2*i-k)^(2*r+k)*binomial(k, i)*(-1)^(r+k-i), i, 0, k/2)), r, 0, n/2-k)/2^(k-1), k, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */

Crossrefs

Sequence in context: A329121 A368765 A073997 * A012572 A371613 A254382

Adjacent sequences: A007115 A007116 A007117 * A007119 A007120 A007121

Keyword

sign,easy

Author

Simon Plouffe

Status

approved