A058807 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.)
1, 1, 6, 396, 420000, 9432450000, 5571367220160000, 103458225408290423193600, 70288262635020872178876253470720, 1993179010286886206697449779415040000000000, 2650683735711909138223088071500675703191552000000000000
Offset: 1
Examples
a(4) = s(4,1)*s(4,2)*s(4,3)*s(4,4) = 6*11*6*1 = 396.
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..36
Programs
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Maple
a:=n->mul(abs(Stirling1(n, k)), k=1..n): seq(a(n), n=1..10); # Zerinvary Lajos, Jun 28 2007
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Mathematica
Abs[Table[Product[StirlingS1[n,k],{k,n}],{n,10}]] (* Harvey P. Dale, Oct 18 2014 *)
Formula
log(a(n)) ~ n^2 * (log(n) + Pi^2/6 - 3/2) / 2. - Vaclav Kotesovec, Feb 27 2021
Extensions
a(11) from Harvey P. Dale, Oct 18 2014