a(n) = Sum_{k=0..n} binomial(2*n+1,4*k).

Terms

a(0) =1a(1) =1a(2) =6a(3) =36a(4) =136a(5) =496a(6) =2016a(7) =8256a(8) =32896a(9) =130816a(10) =523776a(11) =2098176a(12) =8390656a(13) =33550336a(14) =134209536a(15) =536887296a(16) =2147516416a(17) =8589869056a(18) =34359607296a(19) =137439215616a(20) =549756338176