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A007118
Expansion of e.g.f. (1+x)^sin(x).
(Formerly M0916)
1
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).
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
KEYWORD
sign,easy
AUTHOR
STATUS
approved