Number of partitions of n into distinct parts where there are k^2-1 kinds of part k.

Terms

a(0) =1a(1) =0a(2) =3a(3) =8a(4) =18a(5) =48a(6) =109a(7) =264a(8) =594a(9) =1360a(10) =2988a(11) =6552a(12) =14115a(13) =30048a(14) =63288a(15) =131800a(16) =271953a(17) =555792a(18) =1126583a(19) =2264472a(20) =4518051a(21) =8948544a(22) =17603781a(23) =34405272a(24) =66828247a(25) =129040704a(26) =247765665a(27) =473160696a(28) =898924929a(29) =1699331808