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

7,2

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

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);

Crossrefs

Column k=7 of A322383.

Sequence in context: A333109 A208601 A000505 * A179466 A345457 A017773

Adjacent sequences: A332908 A332909 A332910 * A332912 A332913 A332914

Keyword

nonn

Author

Alois P. Heinz, Mar 02 2020

Status

approved