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%I #5 Oct 17 2015 08:36:23
%S 1,1,1,2,3,6,12,28,65,160,408,1074,2898,7998,22508,64426,187251,
%T 551730,1645840,4964876,15130808,46545788,144424944,451715460
%N Number of separate orbits/cycles to which the Catalan bijections A069767/A069768 partition each A000108(n) structures encoded in the range [A014137(n-1)..A014138(n-1)] of the sequence A014486/A063171.
%F a(0)=1, a(n) = (1/(2^(n-1))) * Sum_{i=1..(2^(n-1))} (Sum_{j=0..A007814(i)} A073346(n, j)) = (1/(2^(n-2))) * Sum_{i=1..(2^(n-1))} A073346(n, A007814(i)) - 1 = (1/2^n) * Sum_{i=0..n} (2^(n-i))*A073346(n, i) = Sum_{i=0..n} A074079(n, i)
%p A073431 := proc(n) local i; (1/2^n) * add((2^(n-i))*A073346bi(n,i),i=0..n); end;
%Y Occurs for first time in A073201 as row 6 (and 8). Column sums of the square array A074079/Row sums of the triangle A074080.
%K nonn
%O 0,4
%A _Antti Karttunen_, Jul 31 2002