A387756 - OEIS

A387756

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

1, 5, 46, 468, 4999, 54922, 614576, 6966380, 79724833, 919145823, 10659130596, 124202877644, 1452984920521, 17054550898448, 200751251210208, 2368901534430588, 28013703673441877, 331907593140604813, 3939074720154676802, 46819169533672958440, 557236517853634670494

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..921

FORMULA

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

a(n) = Sum_{k=0..n} (-2)^k * binomial(5*n+2,n-k).

a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(5*n+2,k) * binomial(5*n-k+1,n-k).

a(n) = Sum_{k=0..floor(n/2)} binomial(5*n-2*k,n-2*k).

PROG

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