Binomial transform of A003418.

Terms

a(0) =1a(1) =2a(2) =5a(3) =16a(4) =53a(5) =206a(6) =757a(7) =2780a(8) =10481a(9) =39898a(10) =146981a(11) =531752a(12) =1939885a(13) =7397846a(14) =29864213a(15) =122842036a(16) =488455217a(17) =1830814610a(18) =6508723141a(19) =22667908448a(20) =81343971941a(21) =312864734302