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

10,2

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

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);

Crossrefs

Column k=10 of A322383.

Sequence in context: A332950 A302956 A232080 * A129051 A012039 A286117

Adjacent sequences: A332911 A332912 A332913 * A332915 A332916 A332917

Keyword

nonn

Author

Alois P. Heinz, Mar 02 2020

Status

approved