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 A051675 "Second factorials": Product_{k=1..n} k^(k^2). 17

%I

%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>

%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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Last modified June 6 01:16 EDT 2020. Contains 334858 sequences. (Running on oeis4.)