Binomial transform of rooted tree numbers.

Terms

a(0) =1a(1) =2a(2) =5a(3) =14a(4) =42a(5) =131a(6) =420a(7) =1376a(8) =4589a(9) =15537a(10) =53293a(11) =184881a(12) =647752a(13) =2289215a(14) =8152147a(15) =29226618a(16) =105408688a(17) =382193502a(18) =1392377762a(19) =5094356032a(20) =18711122069a(21) =68965586862a(22) =255006331944a(23) =945662753514