A352901 a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} binomial(n+1,3*k+1) * a(k).

1, 2, 3, 6, 15, 36, 80, 172, 369, 796, 1727, 3774, 8322, 18528, 41643, 94460, 216121, 498186, 1155147, 2689626, 6278841, 14676900, 34316598, 80194032, 187195554, 436310190, 1015176726, 2357708258, 5465611759, 12647864454, 29219750157, 67403414568, 155276809533

Offset

0,2

Comments

Self-convolution of A351970.

Links

Table of n, a(n) for n=0..32.

Formula

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

E.g.f.: d/dx ( exp(x) * Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)! ).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, 3 k + 1] a[k], {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 32}]
nmax = 32; A[_] = 1; Do[A[x_] = A[x^3/(1 - x)^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A040027, A051163, A351970, A352902.

Sequence in context: A100249 A138477 A182240 * A052102 A369628 A053561

Adjacent sequences: A352898 A352899 A352900 * A352902 A352903 A352904

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2022

Status

approved