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%I #20 Apr 20 2024 12:24:27
%S 1,1,4,6912,47552535724032,2344457420244640062508151026483200000,
%T 556518660278190472985800630083758030134707790620313895060688076800000000000000000
%N a(n) = Product_{k=1..n} A000178(k)^k.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Superfactorial.html">Superfactorial</a>.
%F a(n) = Product_{k=1..n} BarnesG(k+2)^k.
%F a(n) = A372140(n+2) / A055462(n)^2.
%F a(n) ~ (2*Pi)^(n*(n+1)*(n+2)/6) * n^(n^4/8 + 7*n^3/12 + 5*n^2/6 + 3*n/8 + 19/720) / (A^(n^2/2 + n/2 - 1/3) * exp(7*n^4/32 + 59*n^3/72 + 17*n^2/24 - n/24 + zeta(3)/(8*Pi^2) + zeta'(-3)/6 - 37/720)), where A is the Glaisher-Kinkelin constant A074962, zeta(3) = A002117, zeta'(-3) = A259068.
%t Table[Product[BarnesG[k+2]^k, {k, 1, n}], {n, 0, 8}]
%Y Cf. A000178, A055462, A255269, A372140.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 20 2024
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