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A332912 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by increasing lengths. 2
1, 73, 2026, 51866, 1205832, 26820444, 590148378, 13100356128, 295439599773, 6807481609901, 160887057723746, 3910224803769926, 97864814302511668, 2524228366327596948, 67113790045849483056, 1839604074821982820944, 51976021537896649002555 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..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, 8)[2]:

seq(a(n), n=8..24);

CROSSREFS

Column k=8 of A322383.

Sequence in context: A224505 A217286 A282784 * A017789 A017736 A221826

Adjacent sequences:  A332909 A332910 A332911 * A332913 A332914 A332915

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 02 2020

STATUS

approved

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Last modified October 31 05:06 EDT 2020. Contains 338098 sequences. (Running on oeis4.)