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%I #4 Jul 13 2020 22:21:11
%S 1,1,5,56,1114,34624,1549648,94402356,7511324448,756406501200,
%T 94039208461584,14146468841290752,2532586289913605088,
%U 532113978869395649856,129662518122880634567232,36270261084908437106586624,11543682123659880166705099776
%N a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k-1)! * a(k).
%F a(n) = (n!)^2 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k*k!)).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
%t nmax = 16; CoefficientList[Series[1/(1 - Sum[x^k/(k k!), {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^2
%t nmax = 16; Assuming[x > 0, CoefficientList[Series[1/(1 + EulerGamma - ExpIntegralEi[x] + Log[x]), {x, 0, nmax}], x]] Range[0, nmax]!^2
%Y Cf. A007840, A102221, A110083, A193161.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 13 2020
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