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

Author

Alois P. Heinz, Apr 27 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..450
• Wikipedia, Permutation

Crossrefs

Column k=6 of A285849.

Cf. A285921.

Programs

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 *)