A390965 a(n) = (1/(n+1)) * Sum_{k=0..n} k^2 * (k+1) * binomial(2*n-k,n-k).

0, 1, 6, 26, 102, 385, 1430, 5278, 19448, 71706, 264860, 980628, 3640210, 13549185, 50565270, 189194550, 709634640, 2667953310, 10052743860, 37957739820, 143606349900, 544321253658, 2066802226236, 7860697923436, 29943415932752, 114230459377300, 436382974714232

Offset

0,3

Links

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

Formula

G.f.: x*g^5 * (1 + x*g), where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[k^2*(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^2*(k+1)*binomial(2*n-k, n-k))/(n+1);
(Magma) [&+[k^2*(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. A099376, A390966, A390967.

Cf. A000108.

Sequence in context: A034560 A307306 A143955 * A256428 A196860 A254317

Adjacent sequences: A390962 A390963 A390964 * A390966 A390967 A390968

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2025

Status

approved