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A309807
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Number of permutations sigma of [n] such that sigma(k)/k > sigma(k+1)/(k+1) for 1 <= k <= n-1.
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4
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1, 1, 1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244, 6437, 14056, 26545, 57326, 109333, 232751, 481137, 1002039, 1911740, 4261276, 8678424, 17734328, 36186279, 77402058, 154454851, 340848002, 691228119, 1460761640
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OFFSET
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0,4
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COMMENTS
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a(n+1) is equal to the number of permutations sigma of [n] such that sigma(k)/k >= sigma(k+1)/(k+1) for 1 <= k <= n-1.
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LINKS
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EXAMPLE
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In case of n = 3.
----+----------
1 | [2, 3, 1]
2 | [3, 2, 1]
In case of n = 4.
----+-------------
1 | [2, 3, 4, 1]
2 | [3, 4, 2, 1]
3 | [4, 3, 2, 1]
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PROG
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(Ruby)
def A(n)
(1..n).to_a.permutation.select{|i| (1..n - 1).all?{|j| i[j - 1] * (j + 1) > i[j] * j}}.size
end
(0..n).map{|i| A(i)}
end
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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