A371756 a(n) = Sum_{k=0..floor(n/3)} binomial(5*n-2*k,n-3*k).

1, 5, 45, 456, 4863, 53383, 597052, 6765471, 77407257, 892270250, 10346070471, 120542238796, 1410040212166, 16549315766244, 194792566133507, 2298472850258746, 27179673132135409, 322013956853586970, 3821532498419234994, 45420775578132979989

Offset

0,2

Links

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

Formula

a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(4*n)).

a(n) ~ 5^(5*n + 5/2) / (99 * sqrt(Pi*n) * 2^(8*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024

a(n) = binomial(5*n, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [(1-5*n)/2, -5*n/2, 1+4*n], -27/4). - Stefano Spezia, Apr 06 2024

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(5*n-2*k, n-3*k));

Crossrefs

Cf. A144904, A371754, A371755.

Sequence in context: A137233 A357205 A001449 * A209442 A371519 A340943

Adjacent sequences: A371753 A371754 A371755 * A371757 A371758 A371759

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved