A390414 a(n) = Sum_{k=0..n} binomial(4*n+2*k+1,n-k).

1, 6, 48, 409, 3583, 31885, 286640, 2595310, 23623866, 215925639, 1980119689, 18207694341, 167804095979, 1549483250640, 14331522047703, 132747501098953, 1231157959401272, 11431218481211305, 106245552661426326, 988381713068035219, 9202313339731774429

Offset

0,2

Links

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

Formula

G.f.: g/((1-4*x*g^3) * (1-x*g^6)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[4*n+2*k+1, 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+1, n-k));

Crossrefs

Cf. A257633, A386811, A390333, A390411, A390412, A390413, A390415, A390416.

Cf. A124820, A390267.

Cf. A002293.

Sequence in context: A385498 A005399 A366942 * A258790 A345077 A244038

Adjacent sequences: A390411 A390412 A390413 * A390415 A390416 A390417

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2025

Status

approved