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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
OFFSET
8,2
LINKS
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 * A361491 A017789 A017736
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 02 2020
STATUS
approved