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A009710
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E.g.f. tan(tan(x)^2) (even powers only).
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2
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0, 2, 16, 512, 34816, 3821312, 618121216, 138682959872, 41171702972416, 15610723195092992, 7357121913006063616, 4217775794187229724672, 2889975739296119171055616, 2332177121915783600628826112
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=4*sum(m=0..n-1/2, ((sum(j=1..2*m+1, j!*2^(2*m-j)*(-1)^(m+1+j)*stirling2(2*m+1,j)))*sum(j=4*m+2..2*n, binomial(j-1,4*m+1)*j!*2^(2*n-j-1)*(-1)^(n+1+j)*stirling2(2*n,j)))/(2*m+1)!). [Vladimir Kruchinin, Jun 21 2011]
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EXAMPLE
| tan(tan(x)*tan(x))=2/2!*x^2+16/4!*x^4+512/6!*x^6+34816/8!*x^8...
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PROG
| (Maxima)
a(n):=4*sum(((sum(j!*2^(2*m-j)*(-1)^(m+1+j)*stirling2(2*m+1, j), j, 1, 2*m+1))*sum(binomial(j-1, 4*m+1)*j!*2^(2*n-j-1)*(-1)^(n+1+j)*stirling2(2*n, j), j, 4*m+2, 2*n))/(2*m+1)!, m, 0, n-1/2); [Vladimir Kruchinin, Jun 21 2011]
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CROSSREFS
| Sequence in context: A168403 A140311 A012389 * A012393 A189899 A189335
Adjacent sequences: A009707 A009708 A009709 * A009711 A009712 A009713
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KEYWORD
| nonn,changed
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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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