A360728 Expansion of Sum_{k>=0} (k * x * (1 + x^3))^k.

1, 1, 4, 27, 257, 3133, 46737, 824567, 16792845, 387700506, 10005766337, 285445919589, 8919587932524, 302975123887680, 11115145723728035, 438000897534309171, 18450681900124075166, 827395845674975999727, 39352977072147424071861

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. A360611, A360727.

Cf. A360731.

Programs

PARI

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

PARI

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

Formula

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