a(n) = Catalan(n)^2*(4n + 3).

Terms

a(0) =3a(1) =7a(2) =44a(3) =375a(4) =3724a(5) =40572a(6) =470448a(7) =5705271a(8) =71571500a(9) =921922716a(10) =12130541488a(11) =162422308412