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

6,2

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

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);

Crossrefs

Column k=6 of A322383.

Sequence in context: A146979 A337904 A278174 * A157722 A010959 A161668

Adjacent sequences: A332907 A332908 A332909 * A332911 A332912 A332913

Keyword

nonn

Author

Alois P. Heinz, Mar 02 2020

Status

approved