Number of ways of piling up n wine bottles above a row of n+1 bottles at ground level.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =16a(6) =43a(7) =115a(8) =303a(9) =813a(10) =2203a(11) =5991a(12) =16371a(13) =44917a(14) =123598a(15) =340988a(16) =942930a(17) =2612735a(18) =7252407a(19) =20163046a(20) =56136326a(21) =156488946a(22) =436739752a(23) =1220157514a(24) =3412116339a(25) =9550192161a(26) =26751643663a(27) =74991516850a(28) =210364915858a(29) =590490257667