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

1,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..36

Formula

log(a(n)) ~ n^2 * (log(n) + Pi^2/6 - 3/2) / 2. - Vaclav Kotesovec, Feb 27 2021

Example

a(4) = s(4,1)*s(4,2)*s(4,3)*s(4,4) = 6*11*6*1 = 396.

Maple

a:=n->mul(abs(Stirling1(n, k)), k=1..n): seq(a(n), n=1..10); # Zerinvary Lajos, Jun 28 2007

Mathematica

Abs[Table[Product[StirlingS1[n, k], {k, n}], {n, 10}]] (* Harvey P. Dale, Oct 18 2014 *)

Crossrefs

Cf. A058808, A132393, A294373.

Sequence in context: A290324 A306887 A289894 * A350017 A000474 A291593

Adjacent sequences: A058804 A058805 A058806 * A058808 A058809 A058810

Keyword

easy,nonn

Author

Leroy Quet, Jan 02 2001

Extensions

a(11) from Harvey P. Dale, Oct 18 2014

Status

approved