A332913 Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

1, 91, 3026, 90597, 2439516, 61989747, 1538707458, 38139479553, 953072924061, 24163160247008, 624376555920980, 16498591390522978, 446749936369626468, 12412653806246040786, 354123558880901036688, 10378353585187092249138, 312512449355524805863371

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..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, 9)[2]:
seq(a(n), n=9..25);

Crossrefs

Column k=9 of A322383.

Sequence in context: A008394 A332949 A221738 * A133416 A169937 A378965

Adjacent sequences: A332910 A332911 A332912 * A332914 A332915 A332916

Keyword

nonn

Author

Alois P. Heinz, Mar 02 2020

Status

approved