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

7,2

Links

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

Crossrefs

Column k=7 of A285849.

Cf. A285922.

Sequence in context: A061619 A185900 A285922 * A203540 A006362 A363176

Adjacent sequences: A285855 A285856 A285857 * A285859 A285860 A285861

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved