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

Terms

a(0) =1a(1) =4a(2) =16a(3) =66a(4) =279a(5) =1203a(6) =5275a(7) =23474a(8) =105853a(9) =483108a(10) =2229253a(11) =10390691a(12) =48879588a(13) =231879456a(14) =1108473015a(15) =5335987930a(16) =25849521109a(17) =125945214309a(18) =616833862018