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A285862 Number of permutations of [2n] with n ordered cycles such that equal-sized cycles are ordered with increasing least elements. 4
1, 1, 19, 1005, 62601, 6061545, 868380535, 142349568361, 27564092244689, 6325532235438273, 1673378033771898675, 505141951803309946125, 170002056228253072537065, 63255335047795174479833625, 25805276337820748477042392695, 11427131417576257617280878155625 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 22 07:40 EDT 2019. Contains 326172 sequences. (Running on oeis4.)