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

Terms

a(0) =1a(1) =4a(2) =12a(3) =44a(4) =176a(5) =672a(6) =2448a(7) =8704a(8) =30528a(9) =105920a(10) =364032a(11) =1241088a(12) =4202752a(13) =14150656a(14) =47410176a(15) =158157824a(16) =525602816a(17) =1740840960a(18) =5748461568a(19) =18930761728a(20) =62190206976a(21) =203850235904a(22) =666838499328