A390332 - OEIS

A390332

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

1, 6, 57, 593, 6430, 71413, 805699, 9191985, 105746033, 1224418350, 14250975939, 166571639207, 1953863362997, 22987383523018, 271145812000410, 3205433903965642, 37968324109901566, 450513569599070651, 5353819430300911362, 63711736023715730830, 759129500826551955561

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OFFSET

0,2

LINKS

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

FORMULA

G.f.: 1/((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,n-k) * Fibonacci(k+1).

MATHEMATICA

Table[Sum[Binomial[5*n+k, 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, n-k));