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%I #11 Jan 17 2019 09:22:06
%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,240248274716697412239360000,
%T 5659588189073370681080838881280000,
%U 148305406398618918682372310424354816000000,4049882681498254991937037064898924144230400000000,137651993399006086593846978063252515678682995490816000000
%N a(n) = Product_{k=1..n} (binomial(k-1,7) + binomial(n-k,7)).
%F a(n) ~ exp(-7*n + (n-7)*(1 + c*Pi)) * n^(7*n) / (7!)^n, where c = 8*cos((Pi + arctan(2769*sqrt(3)/239))/6) / sqrt(21) = 1.2446281707164555154936427017... is the root of the equation 823543*c^6 - 3764768*c^4 + 4302592*c^2 - 692224 = 0.
%t Table[Product[Binomial[k-1,7] + Binomial[n-k,7], {k, 1, n}], {n, 0, 20}]
%o (PARI) a(n) = prod(k=1, n, binomial(k-1, 7) + binomial(n-k, 7)); \\ _Daniel Suteu_, Jan 17 2019
%Y Cf. A000580, A323425, A323496, A323497, A323533, A323534.
%K nonn
%O 0,15
%A _Vaclav Kotesovec_, Jan 17 2019