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

Terms

a(0) =1a(1) =0a(2) =2a(3) =9a(4) =18a(5) =65a(6) =245a(7) =735a(8) =2506a(9) =8784a(10) =29277a(11) =100320a(12) =347589a(13) =1193049a(14) =4123821a(15) =14318759a(16) =49682490a(17) =172830228a(18) =602551604a(19) =2102511006a(20) =7346864653a(21) =25706596155a(22) =90032376546a(23) =315635979373