A332914 Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

1, 111, 4357, 150801, 4654469, 134049203, 3729595473, 102656565841, 2828539643998, 78576462334232, 2212108223706338, 63356175294304198, 1851016172004724086, 55265191691761995338, 1688128671403459821842, 52796230233728968111746, 1691419149055825399281421

Offset: 10

Author

Alois P. Heinz, Mar 02 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=10 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, 10)[2]:
seq(a(n), n=10..26);