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%I #8 Apr 26 2021 12:19:11
%S 1,3,19,182,2328,37234,714674,16004064,409587144,11792756640,
%T 377261048592,13275818803488,509646721402032,21195285059025648,
%U 949279217570464944,45552467588773815744,2331624264279599225088,126804353256754734370176,7301857349340031590836352,443826900013575494233057536
%N a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
%F E.g.f.: 1 / (1 - 2*x + log(1 - x)).
%F a(n) ~ n! / ((2/c + 1 - c) * (1 - c/2)^n), where c = LambertW(2*exp(1)) = 1.3748225281836233816178373171119... - _Vaclav Kotesovec_, Apr 26 2021
%t a[0] = 1; a[n_] := a[n] = 2 n a[n - 1] + Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
%t nmax = 19; CoefficientList[Series[1/(1 - 2 x + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007840, A010842, A052820, A343686, A343687.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 26 2021
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