A351813 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^3) / (1 - x).

1, 1, 2, 7, 32, 179, 1184, 8977, 76391, 719132, 7405261, 82654011, 992533974, 12744345310, 174073918884, 2518084939316, 38429337167618, 616676966998463, 10374679318111371, 182506045254212184, 3349265281648290030, 63984975864984809787, 1270096455615572678617

Offset: 0

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..486

Crossrefs

Cf. A000110, A125273.

Programs

Mathematica

nmax = 22; A[] = 0; Do[A[x] = 1 + x A[x/(1 - x)^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 2 k - 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 22}]

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+2*k-1,n-k-1) * a(k).