A343673 - OEIS

%I #7 Jun 20 2022 03:20:25

%S 1,4,33,409,6759,139621,3460989,100091335,3308146179,123005753041,

%T 5081871122073,230948185830187,11449697796242319,614944043618257237,

%U 35568197580789653685,2204201734650777596863,145703352769994600516187,10233323176300508748808921,761004837938469796089586257

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

%F E.g.f.: 1 / (2 - 3*x - exp(x)).

%F a(n) ~ n! * 3^n / ((1 + LambertW(exp(2/3)/3)) * (2 - 3*LambertW(exp(2/3)/3))^(n+1)). - _Vaclav Kotesovec_, Jun 20 2022

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

%t nmax = 18; CoefficientList[Series[1/(2 - 3 x - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A000670, A005494, A006155, A032032, A343672, A343674.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 25 2021