Number of edge-weighted n-regular multigraphs on 2 unlabeled vertices with total edge weight n.

Terms

a(0) =1a(1) =1a(2) =4a(3) =9a(4) =27a(5) =59a(6) =147a(7) =309a(8) =680a(9) =1359a(10) =2745a(11) =5223a(12) =9923a(13) =18086a(14) =32732a(15) =57515a(16) =100133a(17) =170449a(18) =287377a(19) =475964a(20) =780971a(21) =1262965a(22) =2024448a(23) =3205891a(24) =5035293a(25) =7826984a(26) =12074562a(27) =18460301a(28) =28026831a(29) =42215156