a(n) = Sum_{k=0..n} binomial(k+5,5) * binomial(k,n-k)^2.

Terms

a(0) =1a(1) =6a(2) =27a(3) =140a(4) =651a(5) =2772a(6) =11354a(7) =44640a(8) =169371a(9) =624742a(10) =2248575a(11) =7922124a(12) =27397937a(13) =93214632a(14) =312559200a(15) =1034507696a(16) =3384194616a(17) =10954244952a(18) =35118346760a(19) =111602517096a(20) =351819819414