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%I #26 Feb 27 2021 07:53:28
%S 1,1,6,396,420000,9432450000,5571367220160000,
%T 103458225408290423193600,70288262635020872178876253470720,
%U 1993179010286886206697449779415040000000000,2650683735711909138223088071500675703191552000000000000
%N a(n) = Product_{k=1..n} s(n,k), where s(n,k) is unsigned Stirling number of the first kind. (s(n,k) = number of permutations of n elements which contain exactly k cycles.)
%H Vaclav Kotesovec, <a href="/A058807/b058807.txt">Table of n, a(n) for n = 1..36</a>
%F log(a(n)) ~ n^2 * (log(n) + Pi^2/6 - 3/2) / 2. - _Vaclav Kotesovec_, Feb 27 2021
%e a(4) = s(4,1)*s(4,2)*s(4,3)*s(4,4) = 6*11*6*1 = 396.
%p a:=n->mul(abs(Stirling1(n, k)), k=1..n): seq(a(n), n=1..10); # _Zerinvary Lajos_, Jun 28 2007
%t Abs[Table[Product[StirlingS1[n,k],{k,n}],{n,10}]] (* _Harvey P. Dale_, Oct 18 2014 *)
%Y Cf. A058808, A132393, A294373.
%K easy,nonn
%O 1,3
%A _Leroy Quet_, Jan 02 2001
%E a(11) from _Harvey P. Dale_, Oct 18 2014
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