A351438 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^3.

1, 1, 1, 4, 11, 29, 85, 281, 1003, 3764, 14811, 61327, 267153, 1219497, 5807473, 28763988, 147898511, 788330533, 4349414397, 24799271517, 145904796179, 884577652276, 5519858796807, 35415056743815, 233393746525705, 1578437838849645, 10945142365689985, 77752626344174676

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Formula

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

Mathematica

nmax = 27; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n, k + 2] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 27}]

Crossrefs

Cf. A007476, A045501, A351437.

Sequence in context: A341341 A124861 A369844 * A110579 A361218 A024829

Adjacent sequences: A351435 A351436 A351437 * A351439 A351440 A351441

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 11 2022

Status

approved