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%I #15 Mar 27 2022 03:47:42
%S 1,2,8,54,480,5290,70080,1083614,19145728,380552274,8404669440,
%T 204182993542,5411361939456,155365918497530,4803852288901120,
%U 159142710151610670,5623576097060290560,211138456468635968674,8393550198348236193792,352212802264773650385110
%N Expansion of e.g.f. 1/(1 - 2 * x * cosh(x)).
%F a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%F a(n) ~ n! / ((1 + r * sqrt(1 - 4*r^2)) * r^n), where r = 0.452787214835453627588998503316635625709288535855800416726... is the root of the equation 2*r*cosh(r) = 1. - _Vaclav Kotesovec_, Mar 27 2022
%t With[{m = 19}, Range[0, m]! * CoefficientList[Series[1/(1 - 2*x*Cosh[x]), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x*cosh(x))))
%o (PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));
%Y Cf. A205571, A352649.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 25 2022
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