A368893 a(n) = Sum_{k=0..floor(n/3)} n^(n-2*k) * binomial(n-2*k,k).

1, 1, 4, 30, 288, 3500, 51876, 908607, 18374656, 421492491, 10815040000, 306944040931, 9547373318400, 322972830958648, 11805432990665664, 463673398064821875, 19474259980847153152, 870954834559130974358, 41323803842611198131264

Offset

0,3

Links

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

Formula

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

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

Mathematica

Join[{1}, Table[n^n * HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2 - n/2, -n/2}, -27/(4*n^2)], {n, 1, 20}]] (* Vaclav Kotesovec, Jan 09 2024 *)

Prog

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

Crossrefs

Cf. A368891, A368892.

Cf. A109516, A360727.

Sequence in context: A379187 A379279 A052631 * A301334 A167139 A347994

Adjacent sequences: A368890 A368891 A368892 * A368894 A368895 A368896

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 09 2024

Status

approved