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

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =45a(5) =251a(6) =1624a(7) =11908a(8) =97545a(9) =880660a(10) =8664546a(11) =92096731a(12) =1050304775a(13) =12778138842a(14) =165033693175