A390407 a(n) = Sum_{k=0..n} binomial(4*n-2*k,n-k).

1, 5, 35, 274, 2261, 19228, 166726, 1465399, 13008995, 116374621, 1047384196, 9473049468, 86028257666, 783933555215, 7164492260569, 65642607902166, 602754037713365, 5545405993706068, 51105791195006851, 471704973073493801, 4359800639429095004

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^2)) where g = 1+x*g^4 is the g.f. of A002293.

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

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

Mathematica

Table[Sum[Binomial[4*n-2*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-2*k, n-k));

Crossrefs

Cf. A052203, A066381, A225612, A389361, A389239, A390408, A390409, A390410.

Cf. A006134, A388043.

Cf. A002293.

Sequence in context: A344840 A087630 A388298 * A084135 A229111 A138233

Adjacent sequences: A390404 A390405 A390406 * A390408 A390409 A390410

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2025

Status

approved