A346050 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * A(x/(1 - x)) / (1 - x).

0, 1, 1, 0, 1, 3, 6, 11, 23, 60, 179, 553, 1716, 5415, 17801, 61956, 228391, 882309, 3530322, 14531621, 61454091, 267479778, 1200680113, 5561767211, 26553471186, 130366882251, 656668581417, 3387887246292, 17886582294921, 96603394562849, 533645344137390, 3014295344076655

Offset: 0

Author

Ilya Gutkovskiy, Jul 02 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..695

Crossrefs

Cf. A000994, A000995, A000996, A000997, A000998, A007476, A210540, A346051, A346052.

Programs

Mathematica

nmax = 31; A[] = 0; Do[A[x] = x + x^2 + x^3 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[1] = a[2] = 1; a[n_] := a[n] = Sum[Binomial[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 31}]

SageMath

@CachedFunction
def a(n): # a = A346050
    if (n<3): return (0,1,1)[n]
    else: return sum(binomial(n-3,k)*a(k) for k in range(n-2))
[a(n) for n in range(51)] # G. C. Greubel, Nov 28 2022

Formula

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