a(n) = binomial(4*n,n) - binomial(3*n,n).

Terms

a(0) =0a(1) =1a(2) =13a(3) =136a(4) =1325a(5) =12501a(6) =116032a(7) =1067760a(8) =9782829a(9) =89456455a(10) =817615513a(11) =7475802412a(12) =68416856768a(13) =626891134156