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A009377
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E.g.f. log(1+tan(x)*sin(x)) (even powers only).
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1
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0, 2, -8, 182, -6008, 408122, -38757908, 5438711462, -1008011932208, 244100206825202, -74027819501268908, 27620824218436349342, -12405602584546021488008, 6609444480661620416243882
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=sum(k=1..2*n, ((-1)*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+2*n-2*k-j+1)))*sum(i=0..k/2, (2*i-k)^(2*t+k)*binomial(k,i)*(-1)^(i)))))/(k)). [From Vladimir Kruchinin, Jun 30 2011]
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PROG
| (Maxima)
a(n):=sum(((-1)*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+2*n-2*k-j+1), j, k, 2*n-2*t-k))*sum((2*i-k)^(2*t+k)*binomial(k, i)*(-1)^(i), i, 0, k/2)), t, 0, n-k))/(k), k, 1, 2*n); [From Vladimir Kruchinin, Jun 30 2011]
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CROSSREFS
| Sequence in context: A167009 A105232 A009713 * A181234 A156526 A009505
Adjacent sequences: A009374 A009375 A009376 * A009378 A009379 A009380
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KEYWORD
| sign
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
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