A390973 a(n) = (1/(2*n+1)) * Sum_{k=0..n} k^4 * (2*k+1) * binomial(3*n-k,n-k).

0, 1, 19, 173, 1278, 8684, 56772, 364133, 2313340, 14630265, 92364159, 583015884, 3682815128, 23293263864, 147556696784, 936334841109, 5952158190328, 37904639744195, 241809768144945, 1545250503622245, 9891049394361030, 63412712224839600, 407166098507028432

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: x*g^8 * (1 + 11*x*g^2 + 11*x^2*g^4 + x^3*g^6), where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[k^4*(2*k+1)*Binomial[3*n-k, n-k]/(2*n+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 05 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, k^4*(2*k+1)*binomial(3*n-k, n-k))/(2*n+1);
(Magma) [&+[k^4*(2*k+1)*Binomial(3*n-k, n-k)/(2*n+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 05 2025

Crossrefs

Cf. A390971, A390972.

Cf. A001764.

Sequence in context: A322878 A060222 A041690 * A217698 A172642 A133740

Adjacent sequences: A390970 A390971 A390972 * A390974 A390975 A390976

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2025

Status

approved