Signed recurrence over binary strict trees: a(n) = 1 - Sum_{x + y = n, 0 < x < y < n} a(x) * a(y).

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =1a(5) =0a(6) =0a(7) =1a(8) =0a(9) =0a(10) =1a(11) =-1a(12) =1a(13) =1a(14) =-2a(15) =3a(16) =-1a(17) =-3a(18) =8a(19) =-8a(20) =1a(21) =14a(22) =-26a(23) =22a(24) =10a(25) =-59a(26) =90a(27) =-52a(28) =-74a(29) =238