A360032 Expansion of Sum_{k>=0} (k * x * (1 + (k * x)^3))^k.

1, 1, 4, 27, 257, 3189, 48843, 889079, 18730597, 447945714, 11983618199, 354519428597, 11490618543066, 404910044246256, 15412461332440829, 630199633730994675, 27548323149955792880, 1282044807268698303751, 63284535745130267484867

Offset: 0

Author

Seiichi Manyama, Feb 19 2023

Keywords

• nonn

Crossrefs

Cf. A360018, A360618.

Cf. A360731.

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*binomial(n-3*k, k));

Formula

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