a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(n+2*k-1,n-3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =20a(5) =75a(6) =231a(7) =770a(8) =2988a(9) =11955a(10) =45925a(11) =171897a(12) =647855a(13) =2482753a(14) =9583140a(15) =36942528a(16) =142195548a(17) =548152335a(18) =2118999795a(19) =8207880490a(20) =31824803745a(21) =123488787719a(22) =479622307285