A285856 Number of permutations of [n] with five ordered cycles such that equal-sized cycles are ordered with increasing least elements.

1, 75, 1400, 28700, 431445, 6061545, 101969450, 1511771250, 24207257360, 398261143280, 7126152051200, 125804137586400, 2407653784466640, 47180921713154640, 978889889736934560, 20912829727776156000, 470414513170923511680, 10891943467262968682880

Offset: 5

Author

Alois P. Heinz, Apr 27 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..450
• Wikipedia, Permutation

Crossrefs

Column k=5 of A285849.

Cf. A285920.

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, 6)
    end:
a:= n-> coeff(b(n$2, 0), x, 5):
seq(a(n), n=5..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, 6}];
a[n_] := Coefficient[b[n, n, 0], x, 5];
Table[a[n], {n, 5, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)