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

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

(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));

Crossrefs

Cf. A360018, A360618.

Cf. A360731.

Sequence in context: A360731 A328694 A353015 * A360833 A360835 A374812

Adjacent sequences: A360029 A360030 A360031 * A360033 A360034 A360035

Keyword

nonn

Author

Seiichi Manyama, Feb 19 2023

Status

approved