a(n) = Sum_{k=0..floor(n/4)} binomial(n,4*k)*binomial(5*k,k)/(4*k+1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =6a(6) =16a(7) =36a(8) =76a(9) =172a(10) =436a(11) =1156a(12) =3006a(13) =7606a(14) =19202a(15) =49466a(16) =130156a(17) =345356a(18) =915196a(19) =2421532a(20) =6427001a(21) =17163581a(22) =46087911a(23) =124133531a(24) =334850208a(25) =904691576a(26) =2449891276a(27) =6651540676a(28) =18100561856a(29) =49344295152