Poincaré series [or Poincare series] for depths of roots in a certain root system.

Terms

a(0) =5a(1) =5a(2) =6a(3) =8a(4) =11a(5) =16a(6) =25a(7) =38a(8) =59a(9) =93a(10) =148a(11) =235a(12) =376a(13) =602a(14) =966a(15) =1550a(16) =2491a(17) =4003a(18) =6436a(19) =10348a(20) =16643a(21) =26766a(22) =43052a(23) =69247a(24) =111387a(25) =179169a(26) =288207a(27) =463601a(28) =745744a(29) =1199593