Number of series-reduced balanced rooted trees whose leaves form an integer partition of n.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =9a(5) =19a(6) =31a(7) =63a(8) =110a(9) =215a(10) =391a(11) =773a(12) =1451a(13) =2879a(14) =5594a(15) =11173a(16) =22041a(17) =44136a(18) =87631a(19) =175155a(20) =348186a(21) =694013a(22) =1378911a(23) =2743955a(24) =5452833a(25) =10853541a(26) =21610732a(27) =43122952a(28) =86192274a(29) =172753293