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 A003711 Expansion of e.g.f. cos(tanh(x)) (even powers only). (Formerly M4665) 6
 1, -1, 9, -177, 6097, -325249, 24807321, -2558036145, 342232522657, -57569080467073, 11879658510739497, -2948163649552594737, 865683568087537789297, -296699416391356495667713, 117330699580950022391960505 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..100 FORMULA 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 MATHEMATICA 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 *) PROG (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 */ CROSSREFS Cf. A003710. Sequence in context: A157774 A232694 A193443 * A009009 A220267 A304402 Adjacent sequences: A003708 A003709 A003710 * A003712 A003713 A003714 KEYWORD sign AUTHOR STATUS approved

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)