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

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =11a(5) =41a(6) =189a(7) =1020a(8) =6277a(9) =43262a(10) =328963a(11) =2727076a(12) =24425913a(13) =234743744a(14) =2406904525a(15) =26202132494a(16) =301579542517