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

7,2

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<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);

Crossrefs

Column k=7 of A322384.

Sequence in context: A020766 A069295 A103723 * A287050 A142521 A032630

Adjacent sequences: A332853 A332854 A332855 * A332857 A332858 A332859

Keyword

nonn

Author

Alois P. Heinz, Feb 26 2020

Status

approved