A351812 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 6*x)) / (1 - 6*x)^2.

1, 1, 13, 139, 1531, 19021, 271453, 4358179, 76896931, 1471496341, 30333401893, 670125430219, 15784342627531, 394467249489661, 10415430504486733, 289527454704656659, 8447556960083354131, 258008113711846390981, 8228947382557338981973, 273472796359924298018299

Offset: 0

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

• nonn

Crossrefs

Cf. A005012, A040027, A351756, A351757, A351810, A351811.

Programs

Mathematica

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]
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}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 6^(k-1) * a(n-k).