a(n) is the number of length-n palindromic ballot sequences.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =1a(5) =3a(6) =3a(7) =7a(8) =4a(9) =14a(10) =9a(11) =33a(12) =29a(13) =96a(14) =64a(15) =254a(16) =163a(17) =692a(18) =466a(19) =2140a(20) =1697a(21) =7284a(22) =5161a(23) =24421a(24) =16456a(25) =81892a(26) =55698a(27) =284924a(28) =188134a(29) =1047372