A352861 a(n) = 1 + Sum_{k=0..n-1} binomial(n+2,k+3) * a(k).

1, 2, 7, 28, 121, 570, 2911, 15968, 93433, 580162, 3806275, 26284368, 190415809, 1442982350, 11409436363, 93913277608, 803094241309, 7121757279798, 65383520552131, 620517308328812, 6079168380979213, 61402851498255790, 638674759049919079, 6833589979500278700

Offset: 0

Author

Ilya Gutkovskiy, Apr 06 2022

Keywords

• nonn

Crossrefs

Cf. A000110, A032346, A032347, A045499, A045501, A186021, A352862.

Programs

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n + 2, k + 3] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 23}]
nmax = 23; A[] = 0; Do[A[x] = 1/(1 - x) + x A[x/(1 - x)]/(1 - x)^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x * A(x/(1 - x)) / (1 - x)^4.

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