Number of multigraphs with loops on 4 nodes with n edges.

Terms

a(0) =1a(1) =2a(2) =7a(3) =20a(4) =53a(5) =125a(6) =287a(7) =606a(8) =1226a(9) =2358a(10) =4356a(11) =7740a(12) =13327a(13) =22239a(14) =36151a(15) =57336a(16) =88962a(17) =135249a(18) =201912a(19) =296324a(20) =428211a(21) =609935a(22) =857327a(23) =1190216a(24) =1633551a(25) =2218011a(26) =2981607a(27) =3970548a(28) =5241120a(29) =6861024