Number of Dyck excursions with catastrophes from (0,0) to (n,0).

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =16a(5) =37a(6) =95a(7) =230a(8) =582a(9) =1434a(10) =3606a(11) =8952a(12) =22446a(13) =55917a(14) =140007a(15) =349374a(16) =874150a(17) =2183230a(18) =5460506a(19) =13643972a(20) =34118328a(21) =85270626a(22) =213205958a(23) =532926716a(24) =1332420796a(25) =3330739972a(26) =8327221380a(27) =20816939100a(28) =52043684970a(29) =130105200765