A371744 a(n) = Sum_{k=0..floor(n/2)} binomial(5*n-k,n-2*k).
1, 5, 46, 469, 5017, 55177, 617905, 7008264, 80241790, 925457822, 10735707149, 125128265025, 1464140655619, 17188834766497, 202366206841241, 2388313959181973, 28246993739096305, 334711010978735163, 3972765235517468758, 47224110710958716845
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, binomial(5*n-k, n-2*k));
Formula
a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(4*n)).
a(n) ~ 5^(5*n + 3/2) / (19 * sqrt(Pi*n) * 2^(8*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024