a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)^4.

Terms

a(0) =1a(1) =1a(2) =2a(3) =17a(4) =83a(5) =338a(6) =1923a(7) =11553a(8) =63028a(9) =359203a(10) =2172469a(11) =13026034a(12) =78106885a(13) =478415635a(14) =2957675956a(15) =18321372721a(16) =114301292581a(17) =718253640196