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A285857 Number of permutations of [n] with six ordered cycles such that equal-sized cycles are ordered with increasing least elements. 3
1, 126, 3822, 105336, 2312163, 41420610, 868380535, 16453085220, 312866654100, 6063351173880, 127050688947000, 2603853165950400, 56141875342402480, 1242418296237553440, 28627706535786406800, 683460419058369489600, 16802904218347937067840 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..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, 7)

    end:

a:= n-> coeff(b(n$2, 0), x, 6):

seq(a(n), n=6..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, 7}];

a[n_] := Coefficient[b[n, n, 0], x, 6];

Table[a[n], {n, 6, 25}] (* Jean-Fran├žois Alcover, May 30 2018, from Maple *)

CROSSREFS

Column k=6 of A285849.

Cf. A285921.

Sequence in context: A267750 A285921 A086024 * A036403 A286976 A186816

Adjacent sequences:  A285854 A285855 A285856 * A285858 A285859 A285860

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 27 2017

STATUS

approved

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Last modified September 25 21:49 EDT 2022. Contains 356986 sequences. (Running on oeis4.)