%I M4665 #31 Oct 02 2021 07:56:44
%S 1,-1,9,-177,6097,-325249,24807321,-2558036145,342232522657,
%T -57569080467073,11879658510739497,-2948163649552594737,
%U 865683568087537789297,-296699416391356495667713,117330699580950022391960505
%N Expansion of e.g.f. cos(tanh(x)) (even powers only).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A003711/b003711.txt">Table of n, a(n) for n = 0..100</a>
%F 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
%t 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 *)
%o (Maxima)
%o 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 */
%Y Cf. A003710.
%K sign
%O 0,3
%A _R. H. Hardin_, _Simon Plouffe_