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

Terms

a(0) =1a(1) =3a(2) =6a(3) =19a(4) =69a(5) =267a(6) =1093a(7) =4629a(8) =20142a(9) =89473a(10) =404076a(11) =1849746a(12) =8563558a(13) =40025574a(14) =188612388a(15) =895115942a(16) =4274453904a(17) =20523807009a(18) =99025615998a(19) =479874362583