A390410 a(n) = Sum_{k=0..n} binomial(4*n+4*k,n-k).

1, 5, 41, 361, 3265, 29939, 276801, 2573039, 24008649, 224642600, 2106342663, 19782332254, 186034461253, 1751339312228, 16501658228851, 155597633092530, 1468072425803853, 13858681472700796, 130886412506273100, 1236629034290149157, 11687860045675311275

Offset

0,2

Links

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

Formula

G.f.: 1/((1-4*x*g^3) * (1-x*g^8)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[4*n+4*k, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+4*k, n-k));

Crossrefs

Cf. A052203, A066381, A225612, A389361, A389239, A390407, A390408, A390409.

Cf. A002293.

Sequence in context: A067381 A155612 A145215 * A083884 A156153 A026000

Adjacent sequences: A390407 A390408 A390409 * A390411 A390412 A390413

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2025

Status

approved