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

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =11a(5) =31a(6) =98a(7) =316a(8) =1065a(9) =3649a(10) =12775a(11) =45299a(12) =162713a(13) =590097a(14) =2159015a(15) =7957003a(16) =29517141a(17) =110116277a(18) =412879256a(19) =1555048142a(20) =5880591163a(21) =22319380999a(22) =84992915958a(23) =324634976440