a(n) = Sum_{k=0..n} binomial(k+7,7) * binomial(k,n-k)^2.

Terms

a(0) =1a(1) =8a(2) =44a(3) =264a(4) =1446a(5) =7152a(6) =33516a(7) =149688a(8) =640233a(9) =2642992a(10) =10582220a(11) =41249000a(12) =157050660a(13) =585621960a(14) =2143442400a(15) =7715164176a(16) =27353809188a(17) =95660348904a(18) =330377130644