G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)^4).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =15a(5) =50a(6) =177a(7) =650a(8) =2449a(9) =9412a(10) =36761a(11) =145518a(12) =582556a(13) =2354557a(14) =9594898a(15) =39378259a(16) =162619316a(17) =675258452a(18) =2817643240a(19) =11808576745a(20) =49683880754a(21) =209786559004a(22) =888676860191