G.f. satisfies A(x/(1-x)) = x*(1-sqrt(1-4*A(x)))/(2*A(x)).

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =5a(5) =14a(6) =39a(7) =110a(8) =323a(9) =956a(10) =2835a(11) =8648a(12) =26449a(13) =80356a(14) =253709a(15) =789110a(16) =2400681a(17) =8095578a(18) =24339611a(19) =71349218a(20) =314555855a(21) =559848480a(22) =2096495479a(23) =23012907844a(24) =-84278218251a(25) =415921423864