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%I #10 Mar 28 2019 03:40:33
%S 3,6561,10319560704000000,
%T 47749397192482757629144508002855841842593792000000000
%N a(n) = Product_{i=0..n, j=0..n, k=0..n} (i! + j! + k!).
%C Next term is too long to be included.
%F a(n) ~ c * 2^(n^3/2 + 3*n^2 + 3*n) * 3^n * Pi^(n^3/2 + 3*n^2/2 + 3*n/2) * n^(3*n^4/4 + 3*n^3 + 17*n^2/4 + 5*n/2 + 601/120) / exp(15*n^4/16 + 3*n^3 + 3*n^2 - 21*n/4), where c = 28023.0953536911860317693532637428153075420958129597133...
%t Table[Product[i! + j! + k!, {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 5}]
%t Clear[a]; a[n_] := a[n] = If[n == 0, 3, a[n-1] * Product[k! + j! + n!, {j, 0, n}, {k, 0, n}]^3 * (3*n!) / (Product[k! + 2*n!, {k, 0, n}]^3)]; Table[a[n], {n, 0, 5}]
%Y Cf. A306594, A306729, A324425, A325053.
%K nonn
%O 0,1
%A _Vaclav Kotesovec_, Mar 26 2019
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