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A003711
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Expansion of e.g.f. cos(tanh(x)) (even powers only).
(Formerly M4665)
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6
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1, -1, 9, -177, 6097, -325249, 24807321, -2558036145, 342232522657, -57569080467073, 11879658510739497, -2948163649552594737, 865683568087537789297, -296699416391356495667713, 117330699580950022391960505
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = Sum_{m=1..n} ( Sum_{k=0..2*n-2*m} binomial(2*m+k-1,2*m-1) * (2*m+k)! * (-1)^k * 2^(2*n-2*m-k) * Stirling2(2*n,2*m+k) )/(2*m)!, n>0, a(0)=1. - Vladimir Kruchinin, Jun 10 2011
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MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[Cos[Tanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)
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PROG
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(Maxima)
a(n):=sum((sum(binomial(2*m+k-1, 2*m-1)*(2*m+k)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, 2*m+k), k, 0, 2*n-2*m))/(2*m)!, m, 1, n); /* Vladimir Kruchinin, Jun 10 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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STATUS
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approved
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