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

Terms

a(0) =1a(1) =2a(2) =6a(3) =20a(4) =52a(5) =140a(6) =356a(7) =880a(8) =2123a(9) =5016a(10) =11610a(11) =26400a(12) =59130a(13) =130476a(14) =284216a(15) =611592a(16) =1301344a(17) =2740194a(18) =5713930a(19) =11806144a(20) =24184908a(21) =49142504a(22) =99091244a(23) =198360536a(24) =394342884a(25) =778818658a(26) =1528531702a(27) =2982017956a(28) =5784365082a(29) =11158728448