A390963 a(n) = (1/(n+1)) * Sum_{k=0..n} (k+1)^4 * binomial(2*n-k,n-k).

1, 9, 45, 190, 750, 2871, 10829, 40560, 151470, 565250, 2110482, 7889598, 29541200, 110812275, 416458125, 1568143680, 5915896470, 22359073950, 84655998150, 321071107500, 1219696598484, 4640628968646, 17682523983570, 67471909244640, 257800250487500, 986272572231492

Offset

0,2

Links

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

Formula

G.f.: g^5 * (1 + 4*x*g + x^2*g^2), where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[(k+1)^4*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+1)^4*binomial(2*n-k, n-k))/(n+1);
(Magma) [&+[(k+1)^4 * Binomial(2*n-k, n-k)/(n+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 06 2025

Crossrefs

Cf. A000108, A000245, A070857, A390964.

Sequence in context: A050574 A383912 A124647 * A111640 A024209 A179855

Adjacent sequences: A390960 A390961 A390962 * A390964 A390965 A390966

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2025

Status

approved