OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
KEYWORD
sign,easy
AUTHOR
STATUS
approved