a(n) = Sum_{k=0..n} binomial(k+4,4) * binomial(2*k,2*n-2*k).

Terms

a(0) =1a(1) =5a(2) =20a(3) =125a(4) =610a(5) =2611a(6) =10815a(7) =42610a(8) =161005a(9) =590155a(10) =2106362a(11) =7348265a(12) =25141430a(13) =84569395a(14) =280246795a(15) =916465742a(16) =2961805180a(17) =9470735650a(18) =29994694130a(19) =94172180660a(20) =293326457342a(21) =907028460410