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A232248 Denominators of the expected length of a random cycle in a random permutation. 4
1, 2, 12, 24, 720, 1440, 60480, 4480, 3628800, 1036800, 479001600, 958003200, 2615348736000, 172204032, 2414168064000, 62768369664000, 2462451425280000, 9146248151040000, 51090942171709440000, 136216903680000, 33720021833328230400000, 67440043666656460800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..250

FORMULA

a(n) = Denominator( 1/(n-1)! * Sum_{i=1..n} A132393(n,i)/i ). - Alois P. Heinz, Nov 23 2013

a(n) = denominator(Sum_{k=0..n} A002657(k)/A091137(k)) (conjectured). - Michel Marcus, Jul 19 2019

MAPLE

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      expand(add(multinomial(n, n-i*j, i$j)/j!*(i-1)!^j

      *b(n-i*j, i-1) *x^j, j=0..n/i))))

    end:

a:= n->denom((p->add(coeff(p, x, i)/i, i=1..n))(b(n$2))/(n-1)!):

seq(a(n), n=1..30);  # Alois P. Heinz, Nov 21 2013

# second Maple program:

a:= n-> denom(add(abs(combinat[stirling1](n, i))/i, i=1..n)/(n-1)!):

seq(a(n), n=1..30);  # Alois P. Heinz, Nov 23 2013

MATHEMATICA

Table[Denominator[Total[Map[Total[#]!/Product[#[[i]], {i, 1, Length[#]}]/Apply[Times, Table[Count[#, k]!, {k, 1, Max[#]}]]/(Total[#]-1)!/Length[#]&, Partitions[n]]]], {n, 1, 25}]

CROSSREFS

Numerators are A232193.

Sequence in context: A126962 A002207 A181814 * A091137 A347284 A092825

Adjacent sequences:  A232245 A232246 A232247 * A232249 A232250 A232251

KEYWORD

nonn,frac

AUTHOR

Geoffrey Critzer, Nov 21 2013

STATUS

approved

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Last modified August 9 13:54 EDT 2022. Contains 356026 sequences. (Running on oeis4.)