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A009250
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E.g.f. exp(tan(x)*sin(x)) (even powers only).
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0
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1, 2, 16, 302, 10456, 564842, 43545676, 4528889822, 610057244176, 103185102761042, 21388501828276756, 5328050642207280902, 1569616725144816645016, 539516138161105990193402
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=2*sum(k=1..2*n, sum(t=0..n-k, binomial(2*n,2*t+k)*((sum(j=k..2*n-2*t-k, binomial(j-1,k-1)*j!*stirling2(2*n-2*t-k,j)*(-1)^(n+j)*2^(-2*t-k+2*n-j)))*sum(i=0..k/2, (2*i-k)^(2*t+k)*binomial(k,i)*(-1)^(k-i))))/(2^k*k!)), n>0, a(0)=1. [From Vladimir Kruchinin, Jun 30 2011]
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PROG
| (Maxima)
a(n):=if n=0 then 1 else 2*sum(sum(binomial(2*n, 2*t+k)*((sum(binomial(j-1, k-1)*j!*stirling2(2*n-2*t-k, j)*(-1)^(n+j)*2^(-2*t-k+2*n-j), j, k, 2*n-2*t-k))*sum((2*i-k)^(2*t+k)*binomial(k, i)*(-1)^(k-i), i, 0, k/2)), t, 0, n-k)/(2^k*k!), k, 1, 2*n); [From Vladimir Kruchinin, Jun 30 2011]
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CROSSREFS
| Sequence in context: A189689 A188740 A188985 * A174487 A140051 A189058
Adjacent sequences: A009247 A009248 A009249 * A009251 A009252 A009253
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended and signs tested Mar 15 1997 by Olivier Gerard.
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