Diagonal sums of number triangle [k<=n]*C(n,2n-2k)2^(n-k)A000108(n-k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =1a(5) =6a(6) =9a(7) =12a(8) =41a(9) =60a(10) =121a(11) =310a(12) =505a(13) =1162a(14) =2577a(15) =4760a(16) =11089a(17) =23256a(18) =47089a(19) =107274a(20) =223345a(21) =476366a(22) =1061017a(23) =2237796a(24) =4888313a(25) =10745748a(26) =23048169a(27) =50792638a(28) =111180265a(29) =241786898