a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,2) * binomial(2*k,2*n-4*k).

Terms

a(0) =1a(1) =0a(2) =3a(3) =3a(4) =6a(5) =36a(6) =16a(7) =150a(8) =165a(9) =430a(10) =1071a(11) =1365a(12) =4453a(13) =6258a(14) =14841a(15) =29169a(16) =49941a(17) =115356a(18) =190091a(19) =404811a(20) =750792a(21) =1393956a(22) =2808438a(23) =4988268a(24) =9905746a(25) =18207126a(26) =34231566a(27) =65278964a(28) =119255889a(29) =227648406