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A007118
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E.g.f. (1+x)^sin(x).
(Formerly M0916)
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0
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1, 0, 2, -3, 16, -80, 440, -3171, 24680, -218952, 2170018, -23566675, 279907076, -3603250716, 49968204078, -742893013695, 11785962447792, -198748512229968, 3550002639307890, -66954457199954115, 1329661510693923636
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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. [From Vladimir Kruchinin, Jun 01 2011]
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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); [From Vladimir Kruchinin, Jun 01 2011]
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CROSSREFS
| Sequence in context: A052858 A191416 A073997 * A012572 A067848 A139802
Adjacent sequences: A007115 A007116 A007117 * A007119 A007120 A007121
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KEYWORD
| sign,easy
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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