A323496 a(n) = Product_{k=1..n} (binomial(k-1,3) + binomial(n-k,3)).

1, 0, 0, 0, 0, 0, 1600, 1280000, 1225000000, 1487467520000, 2342962705305600, 4757234928058368000, 12302981968140864000000, 39976163552160000000000000, 161025498138224463853824000000, 794000312545927932130993635328000, 4737527580526919896601692054005760000

Offset: 0

Author

Vaclav Kotesovec, Jan 16 2019

Keywords

• nonn

Crossrefs

Cf. A000292, A323425, A323497, A323533, A323534, A323535.

Programs

Mathematica

Table[Product[Binomial[k-1,3] + Binomial[n-k,3], {k, 1, n}], {n, 0, 20}]

PARI

a(n) = prod(k=1, n, binomial(k-1,3) + binomial(n-k,3)); \\ Michel Marcus, Jan 17 2019

Formula

a(n) ~ exp(2*Pi*(n-3)/3^(3/2) - 2*n - 3) * n^(3*n) / 6^n.