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

Terms

a(0) =0a(1) =18a(2) =100a(3) =425a(4) =1666a(5) =6370a(6) =24228a(7) =92277a(8) =352594a(9) =1351933a(10) =5200130a(11) =20058103a(12) =77558534a(13) =300539938a(14) =1166802820a(15) =4537567325a(16) =17672631538a(17) =68923264009a(18) =269128936778