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%I #17 Sep 08 2022 08:46:19
%S 1,1,16,11664,764411904,7464960000000000,16249593066946560000000000,
%T 11020848942410302096869949440000000000,
%U 3102093199396597590886754340698424229232640000000000,465607547420733489126893933985879279492195953053596584509440000000000
%N a(n) = Product_{k=1..n} k^(2*k).
%H G. C. Greubel, <a href="/A290770/b290770.txt">Table of n, a(n) for n = 0..27</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hyperfactorial.html">Hyperfactorial</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F a(n) = A002109(n)^2.
%F a(n) = A185141(n)/A000178(n-1)^2 for n > 0.
%F a(n) = (n!)^(2*n)/G(n+1)^2, where G() is the Barnes G-function.
%F a(n) ~ A^2*exp(-n^2/2)*n^(n*(n+1))*n^(1/6), where A is the Glaisher-Kinkelin constant (A074962).
%t Table[Product[k^(2 k), {k, 1, n}], {n, 0, 9}]
%t Table[Hyperfactorial[n]^2, {n, 0, 9}]
%t Table[n!^(2 n)/BarnesG[n + 1]^2, {n, 0, 9}]
%o (PARI) a(n) = prod(k=1, n, k^(2*k)) \\ _Felix Fröhlich_, Aug 10 2017
%o (Magma) [1] cat [(&*[k^(2*k): k in [1..n]]): n in [1..10]]; // _G. C. Greubel_, Oct 14 2018
%Y Cf. A000178, A001044, A001818, A002109, A051675, A055209, A061742, A062206, A074962, A184877, A185141, A260122.
%K nonn,easy
%O 0,3
%A _Ilya Gutkovskiy_, Aug 10 2017
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