A368890 a(n) = Sum_{k=0..floor(n/2)} n^(3*(n-2*k)) * binomial(n-k,k).

1, 1, 65, 19737, 16789505, 30525391000, 101570840860033, 558574349855881107, 4722492584690006360065, 58150612359276833311664895, 1000009000028000035000015000001, 23225285520096132372224712190010064, 708804486128121003209727133170234347521

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = [x^n] 1/(1 - n^3*x - x^2).

a(n) ~ n^(3*n). - Vaclav Kotesovec, Jan 09 2024

Mathematica

Join[{1}, Table[n^(3*n) * Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4/n^6], {n, 1, 15}]] (* Vaclav Kotesovec, Jan 09 2024 *)

Prog

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

Crossrefs

Cf. A084845, A176233.

Cf. A368889.

Sequence in context: A323316 A120801 A308697 * A283580 A355496 A308491

Adjacent sequences: A368887 A368888 A368889 * A368891 A368892 A368893

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 09 2024

Status

approved