Total number of nodes in all rooted trees with n nodes.

Terms

a(0) =1a(1) =2a(2) =6a(3) =16a(4) =45a(5) =120a(6) =336a(7) =920a(8) =2574a(9) =7190a(10) =20262a(11) =57192a(12) =162318a(13) =461622a(14) =1317165a(15) =3766096a(16) =10792399a(17) =30980862a(18) =89084844a(19) =256524560a(20) =739658472a(21) =2135213982a(22) =6170505665a(23) =17849399616a(24) =51679366125a(25) =149750549260a(26) =434260826883