a(n) = (7*n+2)*C(n)/(n+2), where C(n) is the n-th Catalan number.

Terms

a(0) =3a(1) =8a(2) =23a(3) =70a(4) =222a(5) =726a(6) =2431a(7) =8294a(8) =28730a(9) =100776a(10) =357238a(11) =1277788a(12) =4605980a(13) =16715250a(14) =61020495a(15) =223931910a(16) =825632610a(17) =3056887680a(18) =11360977650a(19) =42368413620a(20) =158498860260a(21) =594636663660