A332855 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 22, 351, 5119, 73639, 1079354, 16379573, 259470719, 4307274362, 75030122026, 1371391459821, 26279686081517, 527342512678490, 11066063071281662, 242501869570679674, 5541839758896671994, 131891449988832738324, 3264575304106660189788, 83932189324072639925142

Offset: 6

Author

Alois P. Heinz, Feb 26 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 A322384.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
        b(n-i*j, min(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$2, 6)[2]:
seq(a(n), n=6..24);