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

Terms

a(0) =1a(1) =1a(2) =7a(3) =21a(4) =63a(5) =213a(6) =671a(7) =2149a(8) =6911a(9) =22101a(10) =70847a(11) =227045a(12) =727391a(13) =2330901a(14) =7468767a(15) =23931621a(16) =76683583a(17) =245713493a(18) =787329151a(19) =2522806629a(20) =8083720351a(21) =25902323221a(22) =82997717407a(23) =265946059365a(24) =852159682431