Number of inequivalent leaf-colorings of rooted identity trees with n nodes.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =14a(6) =38a(7) =114a(8) =330a(9) =1054a(10) =3483a(11) =11841a(12) =41543a(13) =149520a(14) =552356a(15) =2084896a(16) =8046146a(17) =31649992a(18) =127031001a(19) =518434863a(20) =2153133594a(21) =9081863859a(22) =38909868272a(23) =169096646271a(24) =745348155211