A393228 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^3) / (1 - x)^2.

1, 1, 3, 11, 54, 323, 2241, 17671, 155755, 1512825, 16017287, 183318386, 2252439489, 29539906896, 411465894871, 6061717452230, 94103831065202, 1534537091424337, 26210557169790053, 467745495221383190, 8701568001160424952, 168405853681337658542, 3384457796699512302326

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Mathematica

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

Crossrefs

Cf. A000110, A040027, A045501, A125273, A125274, A351813, A351816, A393227.

Sequence in context: A054700 A009280 A394878 * A267832 A095707 A259105

Adjacent sequences: A393225 A393226 A393227 * A393229 A393230 A393231

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 06 2026

Status

approved