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%I #21 Nov 23 2023 13:23:40
%S 1,1,8,1728,23887872,41278242816000,15407021574586368000000,
%T 1972469516114225950359552000000000,
%U 129292064547357027522197559428775936000000000000
%N a(n) = Product_{k=0...n} (k!^3).
%H Harry J. Smith, <a href="/A061719/b061719.txt">Table of n, a(n) for n=0..27</a>
%F a(n) = a(n-1)*A000442(n). - _R. J. Mathar_, Sep 26 2020
%F From _Vaclav Kotesovec_, Nov 23 2023: (Start)
%F a(n) = A000178(n)^3.
%F a(n) ~ (2*Pi)^(3*n/2 + 3/2) * n^(3*n^2/2 + 3*n + 5/4) / (A^3 * exp(9*n^2/4 + 3*n - 1/4)), where A is the Glaisher-Kinkelin constant A074962. (End)
%t Table[Product[k!^3, {k, 0, n}], {n, 0, 10}] (* _Vaclav Kotesovec_, Nov 23 2023 *)
%o (PARI) for(n=0,11,print(prod(k=1,n,factorial(k)^3)))
%o (PARI) { for (n=0, 27, write("b061719.txt", n, " ", prod(k=2, n, k!^3)) ) } \\ _Harry J. Smith_, Jul 26 2009
%Y Cf. A000178.
%K easy,nonn
%O 0,3
%A _Jason Earls_, Jun 20 2001
%E Terms corrected according to _Jason Earls_'s instructions by _Harry J. Smith_, Jul 26 2009
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