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

Author

Seiichi Manyama, Feb 21 2023

Keywords

• nonn

Crossrefs

Cf. A339481, A360788.

Programs

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));

Formula

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