%I #5 Feb 20 2022 06:46:29
%S 1,1,13,139,1531,19021,271453,4358179,76896931,1471496341,30333401893,
%T 670125430219,15784342627531,394467249489661,10415430504486733,
%U 289527454704656659,8447556960083354131,258008113711846390981,8228947382557338981973,273472796359924298018299
%N G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 6*x)) / (1 - 6*x)^2.
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 6^(k-1) * a(n-k).
%t nmax = 19; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - 6 x)]/(1 - 6 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%Y Cf. A005012, A040027, A351756, A351757, A351810, A351811.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 19 2022