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%I #6 Mar 14 2018 21:21:40
%S 1,0,1,0,1,1,2,2,4,6,10,16,27,46,77,131,224,391,672,1180,2050,3626,
%T 6344,11276,19863,35479,62828,112685,200462,360627,644199,1162296,
%U 2083572,3768866,6777314,12289160,22158106,40255496,72765144,132453122,239936528,437445448
%N Signed recurrence over binary enriched p-trees: a(n) = (-1)^(n-1) + Sum_{x + y = n, 0 < x <= y < n} a(x) * a(y).
%t a[n_]:=a[n]=(-1)^(n-1)+Sum[a[k]*a[n-k],{k,1,n/2}];
%t Array[a,50]
%Y Cf. A000992, A001190, A007317, A063834, A099323, A196545, A220418, A273866, A273873, A289501, A290261, A300352, A300442, A300443, A300862, A300863, A300864, A300866.
%K nonn
%O 1,7
%A _Gus Wiseman_, Mar 13 2018