A287899 Number of permutations of [2n] with exactly n cycles such that the elements of each cycle form an integer interval.

1, 1, 5, 31, 217, 1661, 13721, 121703, 1157857, 11826121, 129877645, 1535504015, 19546846441, 267633414517, 3932330905361, 61806788736551, 1035452546213441, 18421374554192017, 346790652640704725, 6885640002624595007, 143771244649798115257

Offset: 0

Author

Alois P. Heinz, Jun 02 2017

Keywords

• nonn

Comments

All terms are odd.

Examples

			a(2) = 5: (1)(2,3,4), (1)(2,4,3), (1,2)(3,4), (1,2,3)(4), (1,3,2)(4).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..448
• Wikipedia, Permutation

Crossrefs

Cf. A084938, A088218 (analog for set partitions).

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, n!,
       add(b(n-j, i-1)*j!, j=0..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2]*x, 1, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 29 2017 *)
Table[SeriesCoefficient[Sum[k!*x^k, {k, 0, n}]^n, {x,0,n}], {n,0,25}] (* Vaclav Kotesovec, Aug 10 2019 *)

Formula

a(n) = A084938(2n,n).

a(n) = [x^n] (1/(1 - x/(1 - x/(1 - 2*x/(1 - 2*x/(1 - 3*x/(1 - 3*x/(1 - ...))))))))^n, a continued fraction. - Ilya Gutkovskiy, Sep 29 2017

a(n) ~ exp(1) * n * n!. - Vaclav Kotesovec, Sep 29 2017