A285854 Number of permutations of [n] with three ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 18, 105, 1005, 6762, 61572, 558548, 5807700, 62757288, 777291768, 9831740256, 139111566048, 2048834965824, 32758018496640, 545051532176640, 9812211976039680, 182219827628874240, 3627461543458659840, 74765368810365696000, 1632210845693218560000

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..450

Wikipedia, Permutation

Maple

b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
      (p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
      [multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 4)
    end:
a:= n-> coeff(b(n$2, 0), x, 3):
seq(a(n), n=3..25);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 4}];
a[n_] := Coefficient[b[n, n, 0], x, 3];
Table[a[n], {n, 3, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Crossrefs

Column k=3 of A285849.

Cf. A285918.

Sequence in context: A197339 A304763 A322648 * A123277 A123595 A317461

Adjacent sequences: A285851 A285852 A285853 * A285855 A285856 A285857

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved