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

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =29a(5) =141a(6) =520a(7) =1744a(8) =6245a(9) =24781a(10) =101341a(11) =404724a(12) =1578380a(13) =6144334a(14) =24210096a(15) =96377919a(16) =384623541a(17) =1532594677a(18) =6102878893a(19) =24339459250a(20) =97299398849a(21) =389645174251