A332911 Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by increasing lengths.

1, 57, 1297, 28006, 555446, 10718940, 207593322, 4101787080, 83030091003, 1731086543933, 37278557659029, 830606719626674, 19158608403920978, 457571632376980948, 11312327413794558348, 289427158238453113152, 7659193100381954895675, 209516361790095291013179

Offset: 7

Author

Alois P. Heinz, Mar 02 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=7 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, 7)[2]:
seq(a(n), n=7..24);