Number of subpartitions of partition P=[0,0,1,1,1,2,2,2,2,3,3,3,3,3,4,...] (A052146).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =9a(7) =15a(8) =22a(9) =30a(10) =69a(11) =118a(12) =178a(13) =250a(14) =335a(15) =769a(16) =1317a(17) =1995a(18) =2820a(19) =3810a(20) =4984a(21) =11346a(22) =19311a(23) =29126a(24) =41061a(25) =55410a(26) =72492a(27) =92652a(28) =208914a(29) =352636