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

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =4a(5) =10a(6) =6a(7) =0a(8) =28a(9) =144a(10) =270a(11) =220a(12) =286a(13) =1716a(14) =5460a(15) =9100a(16) =10220a(17) =23120a(18) =86496a(19) =217056a(20) =354654a(21) =538650a(22) =1389850a(23) =4108720a(24) =9071062a(25) =15513960a(26) =29008980a(27) =74809800a(28) =192092940a(29) =399254310