%I #13 Apr 27 2024 09:33:50
%S 1,4,864,286654464,7132880358604800000,
%T 993710590042385551668019200000000000,
%U 82086865668400428790437436119503664712777728000000000000000000
%N a(n) = Product_{k=1..n} k!^k.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hyperfactorial.html">Hyperfactorial</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Superfactorial.html">Superfactorial</a>
%F a(n) = A255268(n) / A055462(n-1).
%F a(n) ~ sqrt(A) * exp((3 - 45*n^2 - 32*n^3 - 9*Zeta(3)/Pi^2)/72) * n^((8*n^3 + 18*n^2 + 10*n + 1)/24) * (2*Pi)^(n*(n+1)/4), where A = A074962 = 1.28242712910062263687534256886979... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.2020569031595942853997... .
%t Table[Product[k!^k,{k,1,n}],{n,1,10}]
%t FoldList[Times,Table[(k!)^k,{k,10}]] (* _Harvey P. Dale_, Aug 16 2021 *)
%Y Cf. A000178, A002109, A036740, A055462, A255268.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Feb 20 2015
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