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A285853 Number of permutations of [n] with two ordered cycles such that equal-sized cycles are ordered with increasing least elements. 3
1, 6, 19, 100, 508, 3528, 24876, 219168, 1980576, 21257280, 234434880, 2972885760, 38715943680, 566931294720, 8514866707200, 141468564787200, 2407290355814400, 44753976117043200, 850965783594393600, 17505896073523200000, 367844990453821440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..450

Wikipedia, Permutation

EXAMPLE

a(2) = 1: (1)(2).

a(3) = 6: (1)(23), (23)(1), (2)(13), (13)(2), (3)(12), (12)(3).

a(4) = 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

a:= n-> 2*add(binomial(n, k)*(k-1)!*(n-k-1)!, k=1..n/2)-

        `if`(n::even, 3/2*binomial(n, n/2)*(n/2-1)!^2, 0):

seq(a(n), n=2..25);

# second Maple program:

a:= proc(n) option remember; `if`(n<5, [0, 1, 6, 19][n],

     ((2*n-1)*(n-1)*a(n-1)+(n-2)*(2*n^2-5*n-1)*a(n-2)

      -(n-3)^2*((2*n^2-5*n+4)*a(n-3)+(n-4)^2*a(n-4)))/(2*n))

    end:

seq(a(n), n=2..25);

MATHEMATICA

Table[(n-1)!*(2*HarmonicNumber[n] - (3 + (-1)^n)/n), {n, 2, 25}] (* Vaclav Kotesovec, Apr 29 2017 *)

CROSSREFS

Column k=2 of A285849.

Cf. A285917.

Sequence in context: A151277 A192368 A323686 * A138748 A097899 A223505

Adjacent sequences:  A285850 A285851 A285852 * A285854 A285855 A285856

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 27 2017

STATUS

approved

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Last modified September 25 04:45 EDT 2021. Contains 347652 sequences. (Running on oeis4.)