Number of hierarchical ordered partitions of partitions.

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =17a(5) =38a(6) =87a(7) =191a(8) =421a(9) =911a(10) =1963a(11) =4186a(12) =8885a(13) =18724a(14) =39284a(15) =82005a(16) =170521a(17) =353214a(18) =729290a(19) =1501184a(20) =3081869a(21) =6311404a(22) =12896983a(23) =26301515a(24) =53541702a(25) =108815626a(26) =220824295a(27) =447524559a(28) =905850001a(29) =1831526719