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A309807 Number of permutations sigma of [n] such that sigma(k)/k > sigma(k+1)/(k+1) for 1 <= k <= n-1.

%I A309807 #54 Mar 15 2020 05:53:20
%S A309807 1,1,1,2,3,6,9,19,30,60,108,222,388,874,1601,3244,6437,14056,26545,
%T A309807 57326,109333,232751,481137,1002039,1911740,4261276,8678424,17734328,
%U A309807 36186279,77402058,154454851,340848002,691228119,1460761640
%N A309807 Number of permutations sigma of [n] such that sigma(k)/k > sigma(k+1)/(k+1) for 1 <= k <= n-1.
%C A309807 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.
%H A309807 Mathematics.StackExchange, <a href="https://math.stackexchange.com/questions/3572301/why-are-the-numbers-of-two-different-permutations-the-same">Why are the numbers of two different permutations the same?</a>, Mar 07 2020.
%e A309807 In case of n = 3.
%e A309807 ----+----------
%e A309807   1 | [2, 3, 1]
%e A309807   2 | [3, 2, 1]
%e A309807 In case of n = 4.
%e A309807 ----+-------------
%e A309807   1 | [2, 3, 4, 1]
%e A309807   2 | [3, 4, 2, 1]
%e A309807   3 | [4, 3, 2, 1]
%o A309807 (Ruby)
%o A309807 def A(n)
%o A309807   (1..n).to_a.permutation.select{|i| (1..n - 1).all?{|j| i[j - 1] * (j + 1) > i[j] * j}}.size
%o A309807 end
%o A309807 def A309807(n)
%o A309807   (0..n).map{|i| A(i)}
%o A309807 end
%o A309807 p A309807(10)
%Y A309807 Row sums of A333310.
%Y A309807 Cf. A330432, A332954.
%K A309807 nonn,more
%O A309807 0,4
%A A309807 _Seiichi Manyama_, Mar 03 2020
%E A309807 a(19)-a(22) from _Alois P. Heinz_, Mar 03 2020
%E A309807 a(23)-a(25) from _Giovanni Resta_, Mar 04 2020
%E A309807 a(26)-a(33) from _Bert Dobbelaere_, Mar 15 2020