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%I #22 Sep 08 2022 08:44:59
%S 1,16,314928,1352605460594688,403107840000000000000000000000000,
%T 4157825501361955044460594652554199040000000000000000000000000
%N "Second factorials": Product_{k=1..n} k^(k^2).
%D Spyros G. Kanellos: Mathematical Researches and Results [in Greek]. Athens, 1965.
%H G. C. Greubel, <a href="/A051675/b051675.txt">Table of n, a(n) for n = 1..13</a>
%H Karim Belabas and Henri Cohen, <a href="https://bookstore.ams.org/surv-254/">Numerical Algorithms for Number Theory Using PariGP</a>, American Mathematical Society, 2021, p. 196.
%F a(n) ~ n^(n*(n+1)*(2n+1)/6) / exp(n^3/9 - n/12 - Zeta(3)/(4*Pi^2)), where Zeta(3) = A002117 = 1.2020569031595942853997... . - _Vaclav Kotesovec_, Feb 20 2015
%p A051675 := proc(n) local k; mul(k^(k^2),k=1..n); end;
%t Table[Product[k^(k^2),{k,1,n}],{n,1,10}] (* _Vaclav Kotesovec_, Feb 20 2015 *)
%o (PARI) for(n=1, 10, print1(prod(k=1,n, k^(k^2)), ", ")) \\ _G. C. Greubel_, Oct 14 2018
%o (Magma) [(&*[k^(k^2): k in [1..n]]): n in [1..10]]; // _G. C. Greubel_, Oct 14 2018
%Y Cf. A002109, A255321, A255323, A255344.
%Y Cf. A243262.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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