a(n) = Sum_{i=0..n} C(2*n-i,n+i)*2^i.

Terms

a(0) =1a(1) =2a(2) =8a(3) =30a(4) =116a(5) =452a(6) =1772a(7) =6974a(8) =27524a(9) =108852a(10) =431168a(11) =1709996a(12) =6788536a(13) =26971856a(14) =107235668a(15) =426594110a(16) =1697855876a(17) =6760326116a(18) =26927208368a(19) =107288242820a(20) =427596003416