A285858 Number of permutations of [n] with seven ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 196, 9114, 330750, 10094931, 234138366, 5932023097, 142349568361, 3233779086538, 74147737383720, 1785843031638120, 42966579274786440, 1047584220405271360, 26222209747260881200, 671966452779878874800, 17944599541172975286000, 485789620369911667323360

Offset: 7

Author

Alois P. Heinz, Apr 27 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..450
• Wikipedia, Permutation

Crossrefs

Column k=7 of A285849.

Cf. A285922.

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, 8)
    end:
a:= n-> coeff(b(n$2, 0), x, 7):
seq(a(n), n=7..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, 8}];
a[n_] := Coefficient[b[n, n, 0], x, 7];
Table[a[n], {n, 7, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)