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A330432 Number of permutations sigma of [n] such that k * sigma(k) >= n for 1 <= k <= n.

%I A330432 #32 Mar 03 2020 10:26:24
%S A330432 1,1,1,1,2,4,18,54,384,1920,15000,108000,1270080,8890560,126443520,
%T A330432 1440270720,18811699200,232243200000,4303470124800,56336336179200,
%U A330432 1165698293760000,17784994106880000,349410939842764800,6977881195084800000,173541988447027200000
%N A330432 Number of permutations sigma of [n] such that k * sigma(k) >= n for 1 <= k <= n.
%C A330432 sigma(1) = n and sigma(n) = 1.
%e A330432 In case of n = 4.
%e A330432 ----+-------------
%e A330432   1 | [4, 2, 3, 1]
%e A330432   2 | [4, 3, 2, 1]
%e A330432 In case of n = 5.
%e A330432 ----+----------------
%e A330432   1 | [5, 3, 2, 4, 1]
%e A330432   2 | [5, 3, 4, 2, 1]
%e A330432   3 | [5, 4, 2, 3, 1]
%e A330432   4 | [5, 4, 3, 2, 1]
%o A330432 (Ruby)
%o A330432 def A(n)
%o A330432   (2..n - 1).to_a.permutation.select{|i| (2..n - 1).all?{|j| i[j - 2] * j >= n}}.size
%o A330432 end
%o A330432 def A330432(n)
%o A330432   (0..n).map{|i| A(i)}
%o A330432 end
%o A330432 p A330432(10)
%K A330432 nonn
%O A330432 0,5
%A A330432 _Seiichi Manyama_, Mar 01 2020
%E A330432 a(16)-a(24) from _Giovanni Resta_, Mar 03 2020