G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^6.

Terms

a(0) =1a(1) =1a(2) =6a(3) =33a(4) =236a(5) =1776a(6) =14148a(7) =117070a(8) =995568a(9) =8653068a(10) =76508562a(11) =686035674a(12) =6223653276a(13) =57018806567a(14) =526802616954