A332912 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

1, 73, 2026, 51866, 1205832, 26820444, 590148378, 13100356128, 295439599773, 6807481609901, 160887057723746, 3910224803769926, 97864814302511668, 2524228366327596948, 67113790045849483056, 1839604074821982820944, 51976021537896649002555

Offset: 8

Author

Alois P. Heinz, Mar 02 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=8 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, 8)[2]:
seq(a(n), n=8..24);