A285857 Number of permutations of [n] with six ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 126, 3822, 105336, 2312163, 41420610, 868380535, 16453085220, 312866654100, 6063351173880, 127050688947000, 2603853165950400, 56141875342402480, 1242418296237553440, 28627706535786406800, 683460419058369489600, 16802904218347937067840

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-François 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