Binomial transform of A000013.

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =29a(5) =70a(6) =169a(7) =410a(8) =1005a(9) =2500a(10) =6325a(11) =16276a(12) =42549a(13) =112832a(14) =303073a(15) =823442a(16) =2259917a(17) =6256610a(18) =17451117a(19) =48984114a(20) =138233969a(21) =391876318a(22) =1115233413a(23) =3184379758a(24) =9118632645a(25) =26176992668a(26) =75311867001a(27) =217096296680a(28) =626898050125