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

8,2

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

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);

Crossrefs

Column k=8 of A322383.

Sequence in context: A224505 A217286 A282784 * A361491 A017789 A017736

Adjacent sequences: A332909 A332910 A332911 * A332913 A332914 A332915

Keyword

nonn

Author

Alois P. Heinz, Mar 02 2020

Status

approved