A323538 a(n) = Product_{k=1..n} (binomial(k-1,8) + binomial(n-k,8)).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676788847291127500630565286687890625, 224202413239751513418389758669186941328125000, 81789054189516490351294844356948943677175390625000000, 29455964980491136378751203264203423123185624125549245000000000

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Crossrefs

Cf. A000581, A323425, A323496, A323497, A323533, A323534, A323535.

Programs

Mathematica

Table[Product[Binomial[k-1,8] + Binomial[n-k,8], {k, 1, n}], {n, 0, 20}]

PARI

a(n) = prod(k=1, n, binomial(k-1, 8)+binomial(n-k, 8)) \\ Felix Fröhlich, Jan 17 2019

Formula

a(n) ~ exp(-8*n + (2*sqrt(2+sqrt(2)) - 1/2 - sqrt(2))*Pi*(n-8)) * n^(8*n) / (8!)^n.