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

Terms

a(0) =2a(1) =3a(2) =6a(3) =12a(4) =27a(5) =60a(6) =138a(7) =315a(8) =726a(9) =1668a(10) =3843a(11) =8844a(12) =20370a(13) =46899a(14) =108006a(15) =248700a(16) =572715a(17) =1318812a(18) =3036954a(19) =6993387a(20) =16104246a(21) =37084404a(22) =85397139a(23) =196650348a(24) =452841762a(25) =1042792803a(26) =2401318086a(27) =5529696492a(28) =12733650747a(29) =29322740220