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

0,2

Links

Table of n, a(n) for n=0..19.

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

Prog

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

Crossrefs

Cf. A108081, A371742, A371743.

Sequence in context: A355056 A309185 A169963 * A198256 A232972 A127304

Adjacent sequences: A371741 A371742 A371743 * A371745 A371746 A371747

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved