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%I #16 Apr 14 2023 03:41:34
%S 1,1,8,46656,63403380965376,15407021574586368000000000000000,
%T 1009212044656507725162109374628859215872000000000000000000000,
%U 46564508204734663249790730337537405675293855389346558493242680777666577039360000000000000000000000000000
%N a(n) = (n!)^(n*(n+1)/2).
%F (Product of first n natural numbers )^(sum of first n natural numbers )
%F a(n) ~ (2*Pi)^(n*(n+1)/4) * n^(n*(n+1)*(2*n+1)/4) / exp((n+1)*(12*n^2 - 1)/24). - _Vaclav Kotesovec_, Apr 14 2023
%e a(5) = (5!)^(1+...+5) = 120^15 = 15407021574586368000000000000000. a(6) = 720^21.
%p seq(mul(mul(j^k,j=1..n), k=1..n), n=0..7); # _Zerinvary Lajos_, Jun 02 2007
%t Table[n!^(n(n + 1)/2), {n, 1, 7}]
%o (PARI): for(n=1,7,print1(n!^sum(k=1,n,k),","))
%Y Cf. A000142, A000217.
%K easy,nonn
%O 0,3
%A _Amarnath Murthy_, Jan 02 2002
%E More terms from _Jason Earls_ and _Robert G. Wilson v_, Jan 04 2002
%E a(0)=1 prepended by _Alois P. Heinz_, Nov 13 2018
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