A343686 - OEIS

%I #8 Apr 26 2021 12:19:18

%S 1,4,33,410,6796,140824,3501782,101589732,3368237928,125634319104,

%T 5206805098752,237370661584704,11805144854303760,636030155604374400,

%U 36903603627294958416,2294156656214759133024,152126925169297299197184,10718105879980375520103936,799564645068022035991527552

%N a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

%F E.g.f.: 1 / (1 - 3*x + log(1 - x)).

%F a(n) ~ n! / ((3/c + 2 - c) * (1 - c/3)^n), where c = LambertW(3*exp(2)) = 2.2761339297716461777892556270138... - _Vaclav Kotesovec_, Apr 26 2021

%t a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] + Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]

%t nmax = 18; CoefficientList[Series[1/(1 - 3 x + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A007840, A052820, A053486, A343685, A343687.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 26 2021