A390966 a(n) = (1/(n+1)) * Sum_{k=0..n} k^3 * (k+1) * binomial(2*n-k,n-k).

0, 1, 10, 56, 258, 1089, 4394, 17290, 67048, 257754, 985796, 3759074, 14311750, 54452385, 207163530, 788414010, 3002300400, 11441617950, 43641721260, 166619689080, 636761192964, 2435899184922, 9327702931140, 35753497006596, 137177675480048, 526817306712340

Offset

0,3

Links

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

Formula

G.f.: x*g^6 * (1 + 4*x*g + x^2*g^2), where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[k^3*(k+1)*Binomial[2*n-k, n-k]/(n+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 06 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, k^3*(k+1)*binomial(2*n-k, n-k))/(n+1);
(Magma) [&+[k^3*(k+1)*Binomial(2*n-k, n-k)/(n+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 06 2025

Crossrefs

Cf. A390965, A390967.

Cf. A000108.

Sequence in context: A087076 A014483 A116971 * A200054 A034195 A351458

Adjacent sequences: A390963 A390964 A390965 * A390967 A390968 A390969

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2025

Status

approved