A360813 Expansion of Sum_{k>=0} ( x / (1 - (k * x)^3) )^k.

1, 1, 1, 1, 2, 17, 82, 258, 818, 5671, 43363, 240520, 1183168, 8547054, 77831681, 596258173, 4031934111, 33313129161, 338733239446, 3187239159511, 27197807726066, 260179611473044, 2918973182685904, 31820249821418229, 324099587971865989

Offset

0,5

Links

Table of n, a(n) for n=0..24.

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-(k*x)^3))^k))
(PARI) a(n) = sum(k=0, n\3, (n-3*k)^(3*k)*binomial(n-2*k-1, k));

Crossrefs

Cf. A339481, A360788.

Sequence in context: A215185 A002523 A360747 * A309029 A079889 A053786

Adjacent sequences: A360810 A360811 A360812 * A360814 A360815 A360816

Keyword

nonn

Author

Seiichi Manyama, Feb 21 2023

Status

approved