A390972 a(n) = (1/(2*n+1)) * Sum_{k=0..n} k^3 * (2*k+1) * binomial(3*n-k,n-k).

0, 1, 11, 79, 508, 3148, 19266, 117579, 718520, 4404465, 27102153, 167440548, 1038594736, 6466829512, 40411517734, 253389362883, 1593830672112, 10054759344595, 63604496856285, 403374146069895, 2564226833600460, 16336663435631280, 104295402919919640

Offset

0,3

Links

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

Formula

G.f.: x*g^7 * (1 + 4*x*g^2 + x^2*g^4), where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[k^3*(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^3*(2*k+1)*binomial(3*n-k, n-k))/(2*n+1);
(Magma) [&+[k^3*(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, A390973.

Cf. A001764.

Sequence in context: A243416 A101028 A125348 * A337929 A155619 A126506

Adjacent sequences: A390969 A390970 A390971 * A390973 A390974 A390975

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2025

Status

approved