Generalized Catalan numbers A(x)^2 -(1+x)^2*A(x) +x*(2+x+x^2) =0.

Terms

a(0) =2a(1) =1a(2) =1a(3) =2a(4) =5a(5) =13a(6) =35a(7) =97a(8) =275a(9) =794a(10) =2327a(11) =6905a(12) =20705a(13) =62642a(14) =190987a(15) =586219a(16) =1810011a(17) =5617914a(18) =17518463a(19) =54857506a(20) =172431935a(21) =543861219a(22) =1720737981a(23) =5459867166a(24) =17369553427a(25) =55391735455a(26) =177040109419a(27) =567019562429