A285860 Number of permutations of [n] with nine ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 405, 38610, 2331450, 121706442, 4694535846, 169670838480, 6075923190480, 198663468670953, 6325532235438273, 199912192325692002, 6415747810037718750, 203472294646893246264, 6508361104406113912344, 208391821362083355586128, 6837034161112760255699664

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..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, 10)
    end:
a:= n-> coeff(b(n$2, 0), x, 9):
seq(a(n), n=9..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, 10}];
a[n_] := Coefficient[b[n, n, 0], x, 9];
Table[a[n], {n, 9, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Crossrefs

Column k=9 of A285849.

Cf. A285924.

Sequence in context: A187134 A185839 A285924 * A151634 A132362 A348185

Adjacent sequences: A285857 A285858 A285859 * A285861 A285862 A285863

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved