Number of subpartitions of partition P=[0,1,1,2,2,2,3,3,3,3,4,...] (A003056).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =12a(6) =18a(7) =43a(8) =76a(9) =118a(10) =170a(11) =403a(12) =711a(13) =1107a(14) =1605a(15) =2220a(16) =5188a(17) =9054a(18) =13986a(19) =20171a(20) =27816a(21) =37149a(22) =85569a(23) =147471a(24) =225363a(25) =322075a(26) =440785a(27) =585046a(28) =758814a(29) =1725291