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

0,3

Comments

All terms are odd.

Links

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

Wikipedia, Permutation

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A269730 A036758 A153232 * A110379 A097146 A143020

Adjacent sequences: A287896 A287897 A287898 * A287900 A287901 A287902

Keyword

nonn

Author

Alois P. Heinz, Jun 02 2017

Status

approved