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A226388 Number of n-permutations such that all cycle lengths have a common divisor >= 2. 2
0, 0, 1, 2, 9, 24, 265, 720, 11025, 62720, 965601, 3628800, 130478425, 479001600, 19151042625, 191132125184, 4108830350625, 20922789888000, 1448301616386625, 6402373705728000, 466136852576275881, 5675242696048640000, 193688172394325870625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(p) = (p-1)! for p a prime.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

EXAMPLE

a(6) = 265 counting permutations with cycle types: 6; 4-2; 3-3; 2-2-2; of which there are 120 + 90 + 40 + 15 = 265.

MAPLE

with(combinat):

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

      `if`(i<2, 0, b(n, i-1, g) +`if`(igcd(g, i)<2, 0,

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

         b(n-i*j, i-1, igcd(i, g)), j=1..n/i))))

    end:

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

seq(a(n), n=0..30);  # Alois P. Heinz, Jun 06 2013

MATHEMATICA

f[list_] :=

Total[list]!/Apply[Times, Table[list[[i]], {i, 1, Length[list]}]]/

  Apply[Times,

   Select[Table[

      Count[list, i], {i, 1, Total[list]}], # > 0 &]!]; Table[

Total[Map[f, Select[Partitions[n], Apply[GCD, #] > 1 &]]], {n, 0,

  25}]

CROSSREFS

Cf. A079128.

Sequence in context: A137852 A097346 A261431 * A053194 A005582 A173965

Adjacent sequences:  A226385 A226386 A226387 * A226389 A226390 A226391

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jun 05 2013

STATUS

approved

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Last modified July 5 00:01 EDT 2020. Contains 335457 sequences. (Running on oeis4.)