Number of directed multigraphs with loops on 3 nodes with n arcs.

Terms

a(0) =1a(1) =2a(2) =10a(3) =31a(4) =90a(5) =222a(6) =520a(7) =1090a(8) =2180a(9) =4090a(10) =7356a(11) =12660a(12) =21105a(13) =34020a(14) =53460a(15) =81891a(16) =122826a(17) =180510a(18) =260746a(19) =370370a(20) =518518a(21) =715870a(22) =976170a(23) =1315470a(24) =1753975a(25) =2314936a(26) =3027224a(27) =3923845a(28) =5044920a(29) =6436200