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%I #29 Apr 08 2023 15:02:06
%S 1,2,-4,-88,4496,-155488,675776,903834752,-178181918464,
%T 26154843525632,-2632795710260224,-207121926659381248,
%U 274561534481040183296,-132684091405061956722688,50873850498309673207709696
%N E.g.f. exp(tanh(x)^2) (even powers only).
%H G. C. Greubel, <a href="/A009277/b009277.txt">Table of n, a(n) for n = 0..235</a>
%F a(n) = Sum_{m=1..n} (Sum_{k=0..2*n-2*m} (binomial(k+2*m-1, 2*m-1)*(k+2*m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, k+2*m))/m!). - _Vladimir Kruchinin_, Jun 06 2011
%t nmax = 20; Table[(CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 1, 2*nmax, 2}] (* _Vaclav Kotesovec_, May 27 2022 *)
%t With[{nn=30},Take[CoefficientList[Series[Exp[Tanh[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Apr 08 2023 *)
%o (Maxima) a(n):=sum(sum(binomial(k+2*m-1,2*m-1)*(k+2*m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n,k+2*m),k,0,2*n-2*m)/m!,m,1,n); /* _Vladimir Kruchinin_, Jun 06 2011 */
%o (PARI) x = 'x + O(x^50); select(x->x, Vec(serlaplace(exp(tanh(x)^2)))) \\ _Michel Marcus_, Apr 01 2017
%Y Cf. A000182, A354425.
%K sign
%O 0,2
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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