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A009273
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Expansion of e.g.f. exp(x*tanh(x)) (even powers only).
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8
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1, 2, 4, -24, 400, -5600, -103872, 26975872, -3438685952, 417995260416, -51382607559680, 5994623640856576, -454930757753597952, -94991612229069430784, 81515752167646959124480, -41079088828539119883878400, 18870487103065970636941754368, -8553231336572387307575081566208
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_(m=0..2*n, binomial(2*n,m)*Sum_(k=0..2*n-2*m, binomial(k+m-1,m-1)*(k+m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n-m,k+m))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 06 2011
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MATHEMATICA
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nmax = 20; Table[(CoefficientList[Series[E^(x*Tanh[x]), {x, 0, 2*nmax}], x]*Range[0, 2*nmax]!)[[k]], {k, 1, 2*nmax, 2}] (* Vaclav Kotesovec, May 24 2022 *)
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PROG
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(Maxima)
a(n):=sum(binomial(2*n, m)*sum(binomial(k+m-1, m-1)*(k+m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n-m, k+m), k, 0, 2*n-2*m), m, 0, 2*n); /* Vladimir Kruchinin, Jun 06 2011 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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