A360776 Expansion of Sum_{k>=0} (x * (k + x^3))^k.

1, 1, 4, 27, 257, 3129, 46683, 823799, 16780342, 387467154, 10000823639, 285328449077, 8916487888186, 302885106945216, 11112292144568909, 437902806653498835, 18447046953316227905, 827251374022851280231, 39346845973273509115167

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-4*k) * binomial(n-3*k,k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(k+x^3))^k))
(PARI) a(n) = sum(k=0, n\4, (n-3*k)^(n-4*k)*binomial(n-3*k, k));

Crossrefs

Cf. A360774, A360775.

Cf. A360032, A360728.

Sequence in context: A302108 A240582 A338693 * A360728 A353014 A360731

Adjacent sequences: A360773 A360774 A360775 * A360777 A360778 A360779

Keyword

nonn

Author

Seiichi Manyama, Feb 20 2023

Status

approved