A323497 a(n) = Product_{k=1..n} (binomial(k-1,4) + binomial(n-k,4)).

1, 0, 0, 0, 0, 0, 0, 0, 6890625, 67528125000, 771895089000000, 10758502218240000000, 193672800442598400000000, 4520389860871215408000000000, 136445409183108034775390625000000, 5281556250358583667176941845984375000, 259600586924352252185403119405592275390625

Offset: 0

Author

Vaclav Kotesovec, Jan 16 2019

Keywords

• nonn

Crossrefs

Cf. A000332, A323425, A323496, A323533, A323534, A323535.

Programs

Mathematica

Table[Product[Binomial[k-1,4] + Binomial[n-k,4], {k, 1, n}], {n, 0, 20}]

PARI

a(n) = prod(k=1, n, binomial(k-1,4) + binomial(n-k,4)); \\ Michel Marcus, Jan 17 2019

Formula

a(n) ~ exp(Pi*(sqrt(2) - 1/2)*(n-4) - 4*n) * n^(4*n) / 24^n.