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A285855 Number of permutations of [n] with four ordered cycles such that equal-sized cycles are ordered with increasing least elements. 3
1, 40, 430, 6300, 62601, 706608, 8985560, 107911760, 1439518696, 20364348576, 304923257184, 4772610024000, 80570363703696, 1409795519233536, 26263500315144192, 511153327733815296, 10464902116976779776, 223154458395064842240, 5010190272214829475840 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..450

Wikipedia, Permutation

MAPLE

b:= proc(n, i, p) option remember; series(`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)), x, 5)

    end:

a:= n-> coeff(b(n$2, 0), x, 4):

seq(a(n), n=4..25);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, p_] := b[n, i, p] = Series[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}]], {x, 0, 4}];

a[n_] := Coefficient[b[n, n, 0], x, 4];

Table[a[n], {n, 4, 25}] (* Jean-Fran├žois Alcover, May 30 2018, from Maple *)

CROSSREFS

Column k=4 of A285849.

Cf. A285919.

Sequence in context: A007772 A228122 A247408 * A210355 A210348 A055750

Adjacent sequences:  A285852 A285853 A285854 * A285856 A285857 A285858

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 27 2017

STATUS

approved

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Last modified September 20 06:32 EDT 2021. Contains 347577 sequences. (Running on oeis4.)