"DHK" (bracelet, identity, unlabeled) transform of 3,3,3,3,...

Terms

a(0) =1a(1) =3a(2) =6a(3) =13a(4) =27a(5) =78a(6) =278a(7) =1011a(8) =3753a(9) =13843a(10) =50934a(11) =187629a(12) =692891a(13) =2568882a(14) =9562074a(15) =35742329a(16) =134117829a(17) =505093740a(18) =1908474674a(19) =7232842785a(20) =27486193251a(21) =104712247296a(22) =399816026490