a(n) = 1 + Sum_{k=0..n-2} binomial(n-2,k) * a(k) * a(n-k-2).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =19a(6) =63a(7) =229a(8) =955a(9) =4407a(10) =22445a(11) =124249a(12) =746003a(13) =4821287a(14) =33394193a(15) =246652725a(16) =1935828995a(17) =16086138151a(18) =141100295557