A285859 Number of permutations of [n] with eight ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 288, 19560, 921360, 37423914, 1124673264, 34065856396, 1010435626200, 27564092244689, 746494701977024, 20568917530438368, 575594436161070144, 15985318079107792576, 452561731064312392320, 12942265817549110947520, 383915932720263224659840

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..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, 9)
    end:
a:= n-> coeff(b(n$2, 0), x, 8):
seq(a(n), n=8..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, 9}];
a[n_] := Coefficient[b[n, n, 0], x, 8];
Table[a[n], {n, 8, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Crossrefs

Column k=8 of A285849.

Cf. A285923.

Sequence in context: A048145 A022154 A285923 * A163007 A268873 A069329

Adjacent sequences: A285856 A285857 A285858 * A285860 A285861 A285862

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved