A323534 a(n) = Product_{k=1..n} (binomial(k-1,6) + binomial(n-k,6)).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2551486386077798400, 4356795681519916813516800, 8378295212644383454317143654400, 17729411415388061815791372479702630400, 47314452412112353657024080317791118400000000, 160496342476959706163534573940481304027441961369600

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..115

Crossrefs

Cf. A000579, A323425, A323496, A323497, A323533, A323535.

Programs

Maple

f:= proc(n) local k;  mul(binomial(k-1,6)+binomial(n-k,6),k=1..n) end proc:
map(f, [$0..20]); # Robert Israel, Feb 01 2019

Mathematica

Table[Product[Binomial[k-1,6] + Binomial[n-k,6], {k, 1, n}], {n, 0, 20}]

PARI

a(n) = prod(k=1, n, binomial(k-1, 6) + binomial(n-k, 6)); \\ Daniel Suteu, Jan 17 2019

Formula

a(n) ~ exp(-6*n + (15 - 4*sqrt(3))*Pi*(n-6)/6) * n^(6*n) / (6!)^n.