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A009078
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E.g.f. cos(tan(x)*sin(x)) (even powers only).
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0
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1, 0, -12, -120, -2352, -75840, -1649472, 118634880, 41344643328, 9528901232640, 2213829515240448, 559192086549719040, 156367986602421669888, 48476425507418343751680, 16569615994864645076533248
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=sum(k=1..n, (4^(n-k)*sum(t=k..n-k, binomial(2*n,2*t)*((sum(j=2*k..2*n-2*t, binomial(j-1,2*k-1)*j!*stirling2(2*n-2*t,j)*(-1)^(n+j)*2^(1-j)))*sum(i=0..k, (i-k)^(2*t)*binomial(2*k,i)*(-1)^(k-i)))))/(2*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 sum((4^(n-k)*sum(binomial(2*n, 2*t)*((sum(binomial(j-1, 2*k-1)*j!*stirling2(2*n-2*t, j)*(-1)^(n+j)*2^(1-j), j, 2*k, 2*n-2*t))*sum((i-k)^(2*t)*binomial(2*k, i)*(-1)^(k-i), i, 0, k)), t, k, n-k))/(2*k)!, k, 1, n); [From Vladimir Kruchinin, Jun 30 2011]
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CROSSREFS
| Sequence in context: A012621 A102341 A174561 * A009149 A010570 A012374
Adjacent sequences: A009075 A009076 A009077 * A009079 A009080 A009081
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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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