a(n) = Sum_{k=0..n} binomial(k+6,6) * binomial(k,n-k)^2.

Terms

a(0) =1a(1) =7a(2) =35a(3) =196a(4) =994a(5) =4578a(6) =20118a(7) =84540a(8) =341397a(9) =1335103a(10) =5078227a(11) =18852428a(12) =68519920a(13) =244413820a(14) =857393700a(15) =2963013816a(16) =10102413972a(17) =34025396580a(18) =113329367816a(19) =373642488044