Poincaré series for hyperbolic reflection group with Coxeter diagram shown in Comments.

Terms

a(0) =1a(1) =4a(2) =10a(3) =21a(4) =39a(5) =68a(6) =114a(7) =186a(8) =298a(9) =472a(10) =743a(11) =1165a(12) =1822a(13) =2844a(14) =4434a(15) =6908a(16) =10758a(17) =16749a(18) =26071a(19) =40576a(20) =63146a(21) =98266a(22) =152914a(23) =237948a(24) =370263a(25) =576149a(26) =896514a(27) =1395012a(28) =2170690a(29) =3377668