a(n) = (n+1)*binomial(2n+2,n+1)-3*4^n+binomial(2n,n).

Terms

a(0) =2a(1) =18a(2) =108a(3) =562a(4) =2724a(5) =12660a(6) =57240a(7) =253842a(8) =1109748a(9) =4798780a(10) =20572392a(11) =87580308a(12) =370706408a(13) =1561573032a(14) =6551178288a(15) =27387484242a(16) =114146434068a(17) =474476717292