G.f. (1/x)*Series_Reversion( x*(1-x)*(3 - 2*x + sqrt(1+4*x-4*x^2))/4 ).

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =28a(5) =79a(6) =350a(7) =1075a(8) =5020a(9) =16180a(10) =78023a(11) =259417a(12) =1278340a(13) =4343642a(14) =21740636a(15) =75065787a(16) =380161308a(17) =1328887420a(18) =6792111260a(19) =23975385148a(20) =123448657904a(21) =439228736887