A323533 a(n) = Product_{k=1..n} (binomial(k-1,5) + binomial(n-k,5)).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 790420571136, 100389735898841088, 14582663231533605863424, 2458550581659926554038239232, 529554691027323329170207744475136, 146980847512952623091566575072055001088, 53003014923687519392206631372837133989462016

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Crossrefs

Cf. A000389, A323425, A323496, A323497, A323534, A323535.

Programs

Mathematica

Table[Product[Binomial[k-1,5] + Binomial[n-k,5], {k, 1, n}], {n, 0, 20}]

PARI

a(n) = prod(k=1, n, binomial(k-1,5) + binomial(n-k,5)); \\ Michel Marcus, Jan 17 2019

Formula

a(n) ~ exp((1 + 2*Pi*sqrt(5 - 2/sqrt(5))/5) * (n-5)) * n^(5*n) / (exp(5*n)*120^n).