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

Terms

a(0) =1a(1) =4a(2) =19a(3) =94a(4) =470a(5) =2357a(6) =11829a(7) =59368a(8) =297902a(9) =1494469a(10) =7495425a(11) =37584962a(12) =188432209a(13) =944567955a(14) =4734350650a(15) =23727223169a(16) =118905239428a(17) =595839590228