A332913 Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

1, 91, 3026, 90597, 2439516, 61989747, 1538707458, 38139479553, 953072924061, 24163160247008, 624376555920980, 16498591390522978, 446749936369626468, 12412653806246040786, 354123558880901036688, 10378353585187092249138, 312512449355524805863371

Offset: 9

Author

Alois P. Heinz, Mar 02 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=9 of A322383.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
        b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]
         (n, i$j, n-i*j)), j=0..n/i)))
    end:
a:= n-> b(n, 1, 9)[2]:
seq(a(n), n=9..25);