G.f. satisfies A(x) = 1/(1 - 4*x) - x*A(x)^3.

Terms

a(0) =1a(1) =3a(2) =7a(3) =16a(4) =55a(5) =235a(6) =856a(7) =2664a(8) =9055a(9) =37417a(10) =151431a(11) =533452a(12) =1825972a(13) =7141860a(14) =29778280a(15) =113688592a(16) =400940751a(17) =1499506693a(18) =6185139781a(19) =24862774872a(20) =91529003839a(21) =334939413067