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A196301 The number of ways to linearly order the cycles in each permutation of {1,2,...,n} where two cycles are considered identical if they have the same length. 3
1, 1, 2, 9, 44, 270, 2139, 18837, 186808, 2070828, 25861140, 350000640, 5145279611, 81492295079, 1381583542234, 25097285838765, 484602684624080, 9894705390149400, 213418984780492164, 4842425874827849868, 115231446547162291200, 2874808892527026177240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..444

EXAMPLE

a(4) = 44 because in the conjugacy classes of S(4): (4), (3)(1), (2)(2), (2)(1)(1), (1)(1)(1)(1) there are (respectively) 6 permutations times 1 arrangement, 8 permutations times 2 arrangements, 3 permutations times 1 arrangement, 6 permutations times 3 arrangements, and 1 permutation times 1 arrangement.  So 6*1+8*2+3*1+6*3+1*1 = 44.

MAPLE

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

      (p+n)!/n!, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat

      [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..25);  # Alois P. Heinz, Apr 27 2017

MATHEMATICA

Needs["Combinatorica`"]; f[{x_, y_}]:= x^y y!; Table[Total[Table[n!, {PartitionsP[n]}]/Apply[Times, Map[f, Map[Tally, Partitions[n]], {2}], 2] * Apply[Multinomial, Map[Last, Map[Tally, Partitions[n]], {2}], 2]], {n, 0, 20}]

CROSSREFS

Cf. A120774.

Row sums of A285849.

Sequence in context: A000166 A093464 A308338 * A331559 A184932 A073478

Adjacent sequences:  A196298 A196299 A196300 * A196302 A196303 A196304

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Sep 30 2011

STATUS

approved

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)