A360731 Expansion of Sum_{k>=0} (k * x * (1 + k*x^3))^k.

1, 1, 4, 27, 257, 3141, 46899, 827639, 16855357, 389100834, 10040378183, 286386193685, 8947506702834, 303875954083536, 11146559606379269, 439178938765108083, 18497974976610341624, 829420114454360154295, 39445018962975879216867

Offset: 0

Author

Seiichi Manyama, Feb 18 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A360618, A360730.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+k*x^3))^k))

PARI

a(n) = sum(k=0, n\4, (n-3*k)^(n-2*k)*binomial(n-3*k, k));

Formula

a(n) = Sum_{k=0..floor(n/4)} (n-3*k)^(n-2*k) * binomial(n-3*k,k).