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

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..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, 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 *)

Crossrefs

Column k=5 of A285849.

Cf. A285920.

Sequence in context: A293581 A210047 A210505 * A202257 A278154 A017791

Adjacent sequences: A285853 A285854 A285855 * A285857 A285858 A285859

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2017

Status

approved