A285862 Number of permutations of [2n] with n ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 1, 19, 1005, 62601, 6061545, 868380535, 142349568361, 27564092244689, 6325532235438273, 1673378033771898675, 505141951803309946125, 170002056228253072537065, 63255335047795174479833625, 25805276337820748477042392695, 11427131417576257617280878155625

Offset

0,3

Links

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

Wikipedia, Permutation

Formula

a(n) = A285849(2n,n).

Example

a(1) = 1: (12).
a(2) = 19: (123)(4), (4)(123), (132)(4), (4)(132), (124)(3), (3)(124), (142)(3), (3)(142), (134)(2), (2)(134), (143)(2), (2)(143), (1)(234), (234)(1), (1)(243), (243)(1),  (12)(34), (13)(24), (14)(23).

Maple

b:= proc(n, i, p) option remember; expand(`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)))
    end:
a:= n-> coeff(b(2*n$2, 0), x, n):
seq(a(n), n=0..20);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Expand[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}]]];
a[n_] := Coefficient[b[2n, 2n, 0], x, n];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 29 2018, from Maple *)

Crossrefs

Cf. A187646, A285849, A285926.

Sequence in context: A247279 A192569 A238740 * A136022 A203582 A136021

Adjacent sequences: A285859 A285860 A285861 * A285863 A285864 A285865

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved