A390268 a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,n-k).

1, 4, 19, 94, 470, 2357, 11829, 59368, 297902, 1494469, 7495425, 37584962, 188432209, 944567955, 4734350650, 23727223169, 118905239428, 595839590228, 2985639571718, 14959922129662, 74956381227810, 375558759884508, 1881652000369616, 9427455976971208, 47232924151619828

Offset

0,2

Links

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

Formula

G.f.: c(x)/( sqrt(1-4*x) * (1-x*c(x)^5) ), where c(x) is the g.f. of A000108.

Mathematica

Table[Sum[Binomial[2*n+3*k+1, n-k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 04 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, n-k));

Crossrefs

Cf. A000302, A001791, A079309, A390266, A390267.

Cf. A000108, A360144.

Sequence in context: A122369 A005978 A083065 * A137636 A027618 A278678

Adjacent sequences: A390265 A390266 A390267 * A390269 A390270 A390271

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2025

Status

approved