a(n) = 3*binomial(2n, n-1)/(n+2), n > 0, with a(0)=1.

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =28a(5) =90a(6) =297a(7) =1001a(8) =3432a(9) =11934a(10) =41990a(11) =149226a(12) =534888a(13) =1931540a(14) =7020405a(15) =25662825a(16) =94287120a(17) =347993910a(18) =1289624490a(19) =4796857230a(20) =17902146600a(21) =67016296620a(22) =251577050010a(23) =946844533674