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

Terms

a(0) =1a(1) =1a(2) =2a(3) =8a(4) =30a(5) =98a(6) =303a(7) =937a(8) =2936a(9) =9260a(10) =29209a(11) =91999a(12) =289547a(13) =911255a(14) =2868341a(15) =9029425a(16) =28424456a(17) =89478064a(18) =281667368a(19) =886657848a(20) =2791106585a(21) =8786123349a(22) =27657838272a(23) =87064092870a(24) =274068969337a(25) =862741412709