Partial sums of "Half-Catalan numbers" A000992.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =8a(5) =14a(6) =25a(7) =49a(8) =96a(9) =199a(10) =413a(11) =894a(12) =1924a(13) =4261a(14) =9392a(15) =21205a(16) =47534a(17) =108492a(18) =246313a(19) =568003a(20) =1302431a(21) =3024429a(22) =6990985a(23) =16343338a(24) =38026783a(25) =89322813a(26) =208986625a(27) =493184761a(28) =1159317065a(29) =2745547588