A320168 - OEIS

%I #41 Oct 21 2018 04:10:59

%S 1,1,2,2,7,12,22,26,85,226,717,1695,5071,14275,47405,176747,638329,

%T 2166516

%N Number of ways to group the first 2*n positive integers into n pairs (xi, yi) with xi < yi, and such that the n numbers (yi mod xi) are all different.

%C How does a(n+1)/a(n) behave as n increases?

%H David A. Corneth, <a href="/A320168/a320168_2.png">Illustration for a(4)</a>

%e a(3) = 2 because {(1,3), (2,5), (4,6)} and {(1,5), (2,3), (4,6)} are corresponding sets.

%e a(4) = 7 because {(1,6), (2,5), (3,8), (4,7)}, {(1,3), (2,7), (4,6), (5,8)}, {(1,7), (2,3), (4,6), (5,8)}, {(1,3), (2,5), (4,7), (6,8)}, {(1,5), (2,3), (4,7), (6,8)}, {(1,2), (3,7), (4,6), (5,8)}, {(1,2), (3,8), (4,7), (5,6)} are corresponding sets.

%Y Cf. A002968, A060963, A272363, A320129.

%K nonn,more

%O 0,3

%A _Altug Alkan_, Oct 07 2018

%E a(13)-a(17) from _Rémy Sigrist_, Oct 07 2018