Vacation Dyck paths. Discrete analog for vacation M/M/1 queue embedded chain.

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =0a(5) =2a(6) =1a(7) =5a(8) =4a(9) =15a(10) =14a(11) =48a(12) =49a(13) =159a(14) =173a(15) =540a(16) =616a(17) =1869a(18) =2211a(19) =6565a(20) =7994a(21) =23335a(22) =29092a(23) =83756a(24) =106489a(25) =303093a(26) =391815a(27) =1104490a(28) =1448313a(29) =4049108