a(n) = C(n)*(6*n + 1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =7a(2) =26a(3) =95a(4) =350a(5) =1302a(6) =4884a(7) =18447a(8) =70070a(9) =267410a(10) =1024556a(11) =3938662a(12) =15184876a(13) =58689100a(14) =227327400a(15) =882230895a(16) =3429693990a(17) =13353413370a(18) =52062618300a(19) =203235266850a(20) =794258570820