A371744 - OEIS

%I #12 Apr 05 2024 13:06:28

%S 1,5,46,469,5017,55177,617905,7008264,80241790,925457822,10735707149,

%T 125128265025,1464140655619,17188834766497,202366206841241,

%U 2388313959181973,28246993739096305,334711010978735163,3972765235517468758,47224110710958716845

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

%F a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(4*n)).

%F a(n) ~ 5^(5*n + 3/2) / (19 * sqrt(Pi*n) * 2^(8*n - 1/2)). - _Vaclav Kotesovec_, Apr 05 2024

%o (PARI) a(n) = sum(k=0, n\2, binomial(5*n-k, n-2*k));

%Y Cf. A108081, A371742, A371743.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 05 2024