Number of partitions of the (n+3)-multiset {0,...,0,1,2,3} with n 0's into distinct multisets.

Terms

a(0) =5a(1) =15a(2) =31a(3) =59a(4) =100a(5) =161a(6) =249a(7) =372a(8) =539a(9) =765a(10) =1066a(11) =1460a(12) =1972a(13) =2629a(14) =3466a(15) =4526a(16) =5856a(17) =7513a(18) =9569a(19) =12102a(20) =15208a(21) =19001a(22) =23610a(23) =29186a(24) =35908a(25) =43980a(26) =53639a(27) =65162a(28) =78864a(29) =95107