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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =16a(6) =75a(7) =309a(8) =1183a(9) =4360a(10) =15783a(11) =56750a(12) =203929a(13) =734722a(14) =2658071a(15) =9662093a(16) =35292151a(17) =129513736a(18) =477376575a(19) =1766738922a(20) =6563071865a(21) =24464169890a(22) =91478369359a(23) =343051225066