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A332858 Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by decreasing lengths. 2
1, 46, 1376, 34662, 808029, 18239040, 408622073, 9219406943, 211361047584, 4951434599465, 118953031062221, 2937244849150543, 74649387584172199, 1954230833420758243, 52717076107348326739, 1465510610406405412331, 41979421676766533788251, 1238736596075658751908901 (list; graph; refs; listen; history; text; internal format)
OFFSET
9,2
LINKS
Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
Wikipedia, Permutation
MAPLE
b:= proc(n, l) option remember; `if`(n=0, l[9], add((j-1)!*b(n-j,
sort([l[], j], `>`)[1..9])*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, [0$9]):
seq(a(n), n=9..26);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 0, l[[9]], Sum[(j-1)! b[n-j, ReverseSort[ Append[l, j]][[1 ;; 9]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, Table[0, {9}]];
a /@ Range[9, 26] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)
CROSSREFS
Column k=9 of A322384.
Sequence in context: A302767 A078195 A103725 * A264505 A308101 A291129
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 26 2020
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)