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A332859
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Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
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2
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1, 56, 1992, 58566, 1569387, 40210458, 1011778943, 25407870031, 643294838111, 16530707226038, 433032539982493, 11597633757170403, 318186179384754262, 8953723541105483282, 258628065642282683675, 7671629851218367059371, 233734404206144319940526
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OFFSET
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10,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 10..450
Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
Wikipedia, Permutation
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MAPLE
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b:= proc(n, l) option remember; `if`(n=0, l[10], add((j-1)!*b(n-j,
sort([l[], j], `>`)[1..10])*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, [0$10]):
seq(a(n), n=10..27);
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MATHEMATICA
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b[n_, l_] := b[n, l] = If[n == 0, l[[10]], Sum[(j-1)!*b[n-j, ReverseSort[ Append[l, j]][[1 ;; 10]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, Table[0, {10}]];
a /@ Range[10, 27] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)
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CROSSREFS
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Column k=10 of A322384.
Sequence in context: A038649 A004375 A103726 * A004387 A111597 A111781
Adjacent sequences: A332856 A332857 A332858 * A332860 A332861 A332862
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Feb 26 2020
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STATUS
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approved
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