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A332853
Number of entries in the fourth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
3
1, 11, 101, 932, 9185, 98317, 1141614, 14297174, 192303794, 2767778378, 42482344932, 692989979996, 11977186926515, 218693683265139, 4207257180352118, 85067513019575426, 1803695291827381964, 40022639769763695724, 927602835889551674104, 22416055484058795043176
OFFSET
4,2
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[4], add((j-1)!*b(n-j,
sort([l[], j], `>`)[1..4])*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, [0$4]):
seq(a(n), n=4..24);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 0, l[[4]], Sum[(j-1)! b[n-j, ReverseSort[ Append[l, j]][[1 ;; 4]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, {0, 0, 0, 0}];
a /@ Range[4, 24] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A322384.
Sequence in context: A138894 A287832 A122105 * A289850 A351811 A171750
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 26 2020
STATUS
approved