G.f. A(x) satisfies A(x) = 1 + x/(1+x^2)^2 * A(x)^2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =15a(6) =40a(7) =110a(8) =310a(9) =891a(10) =2602a(11) =7699a(12) =23032a(13) =69547a(14) =211692a(15) =648861a(16) =2000998a(17) =6204133a(18) =19328474a(19) =60475420a(20) =189950398a(21) =598718725a(22) =1893169916a(23) =6003728385a(24) =19090291408a(25) =60851602621a(26) =194409662846a(27) =622411297884