a(n) = (5n+2)*C(n) where C(n) = Catalan numbers (A000108).

Terms

a(0) =2a(1) =7a(2) =24a(3) =85a(4) =308a(5) =1134a(6) =4224a(7) =15873a(8) =60060a(9) =228514a(10) =873392a(11) =3350802a(12) =12896744a(13) =49774300a(14) =192559680a(15) =746503065a(16) =2899328940a(17) =11279096730a(18) =43942760400a(19) =171424529430a(20) =669540282840