A285861 Number of permutations of [n] with ten ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 550, 71225, 5448300, 355885530, 17364367020, 748875613200, 31800834780000, 1237174959934485, 46053097166277630, 1673378033771898675, 61000413008705597700, 2201843172941618228220, 79401490178154061870920, 2850407051830237872094980

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..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, 11)
    end:
a:= n-> coeff(b(n$2, 0), x, 10):
seq(a(n), n=10..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, 11}];
a[n_] := Coefficient[b[n, n, 0], x, 10];
Table[a[n], {n, 10, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Crossrefs

Column k=10 of A285849.

Cf. A285925.

Sequence in context: A190075 A234415 A285925 * A034282 A127347 A351664

Adjacent sequences: A285858 A285859 A285860 * A285862 A285863 A285864

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved