A390385 - OEIS

A390385

a(n) = Sum_{k=0..n} binomial(n+5*k,k).

1, 7, 74, 903, 11696, 156412, 2134115, 29523727, 412593538, 5810801734, 82338880809, 1172531129996, 16765684193304, 240553723047659, 3461594129422699, 49938834336302123, 722033914592129473, 10459673068988940014, 151783335395668575448, 2205947647778842429966

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OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..700

FORMULA

G.f.: 1/((1-6*x*g^5) * (1-x*g)) where g = 1+x*g^6 is the g.f. of A002295.

a(n) ~ 2^(6*n+5) * 3^(6*n + 11/2) / (7151 * sqrt(Pi*n) * 5^(5*n + 1/2)). - Vaclav Kotesovec, Nov 04 2025

MATHEMATICA

Table[Sum[Binomial[n+5*k, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 04 2025 *)

PROG

(PARI) a(n) = sum(k=0, n, binomial(n+5*k, k));