A332855 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 22, 351, 5119, 73639, 1079354, 16379573, 259470719, 4307274362, 75030122026, 1371391459821, 26279686081517, 527342512678490, 11066063071281662, 242501869570679674, 5541839758896671994, 131891449988832738324, 3264575304106660189788, 83932189324072639925142

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<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, 6)[2]:
seq(a(n), n=6..24);

Crossrefs

Column k=6 of A322384.

Sequence in context: A103722 A100904 A036738 * A054940 A016265 A208458

Adjacent sequences: A332852 A332853 A332854 * A332856 A332857 A332858

Keyword

nonn

Author

Alois P. Heinz, Feb 26 2020

Status

approved