A332910 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

1, 43, 785, 14065, 234646, 3890624, 65790726, 1149152226, 20755593249, 389723127653, 7616467493381, 155034653456005, 3285524611730078, 72467273447829602, 1661985062849397148, 39610017536621076924, 979981089604037392299, 25145506663601266049403

Offset: 6

Author

Alois P. Heinz, Mar 02 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=6 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, 6)[2]:
seq(a(n), n=6..23);