A390334 - OEIS

A390334

a(n) = Sum_{k=0..n} binomial(5*n+k+1,n-k).

1, 7, 68, 715, 7803, 87043, 985193, 11267400, 129874340, 1506178906, 17553447669, 205400423279, 2411613715503, 28396270144675, 335187835505831, 3965053954826227, 46992669349170667, 557875506832484689, 6632725792265069990, 78963785195893968275, 941214087799404662551

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OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..800

FORMULA

G.f.: g/((1-5*x*g^4) * (1-x*g^6)) where g = 1+x*g^5 is the g.f. of A002294.

a(n) = Sum_{k=0..n} binomial(5*n+1,n-k) * Fibonacci(k+1).

MATHEMATICA

Table[Sum[Binomial[5*n+k+1, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

PROG

(PARI) a(n) = sum(k=0, n, binomial(5*n+k+1, n-k));