A332856 Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 29, 583, 10366, 177299, 3029643, 52724894, 944353801, 17510885251, 337239557401, 6756438503137, 140893616636126, 3057901614671778, 69040616816923804, 1620394508763080044, 39500148841295346478, 999160362731046844470, 26200784568622019301658

Offset: 7

Author

Alois P. Heinz, Feb 26 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 A322384.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
        b(n-i*j, min(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$2, 7)[2]:
seq(a(n), n=7..24);