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

Terms

a(0) =1a(1) =5a(2) =35a(3) =274a(4) =2261a(5) =19228a(6) =166726a(7) =1465399a(8) =13008995a(9) =116374621a(10) =1047384196a(11) =9473049468a(12) =86028257666a(13) =783933555215