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A287899 Number of permutations of [2n] with exactly n cycles such that the elements of each cycle form an integer interval. 6
1, 1, 5, 31, 217, 1661, 13721, 121703, 1157857, 11826121, 129877645, 1535504015, 19546846441, 267633414517, 3932330905361, 61806788736551, 1035452546213441, 18421374554192017, 346790652640704725, 6885640002624595007, 143771244649798115257 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 13:20 EST 2022. Contains 350511 sequences. (Running on oeis4.)