%I #9 Jan 17 2019 09:22:13
%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,676788847291127500630565286687890625,
%T 224202413239751513418389758669186941328125000,
%U 81789054189516490351294844356948943677175390625000000,29455964980491136378751203264203423123185624125549245000000000
%N a(n) = Product_{k=1..n} (binomial(k-1,8) + binomial(n-k,8)).
%F a(n) ~ exp(-8*n + (2*sqrt(2+sqrt(2)) - 1/2 - sqrt(2))*Pi*(n-8)) * n^(8*n) / (8!)^n.
%t Table[Product[Binomial[k-1,8] + Binomial[n-k,8], {k, 1, n}], {n, 0, 20}]
%o (PARI) a(n) = prod(k=1, n, binomial(k-1, 8)+binomial(n-k, 8)) \\ _Felix Fröhlich_, Jan 17 2019
%Y Cf. A000581, A323425, A323496, A323497, A323533, A323534, A323535.
%K nonn
%O 0,17
%A _Vaclav Kotesovec_, Jan 17 2019