Number of Dyck paths of length 2n with exactly 1 hill.

Terms

a(0) =0a(1) =1a(2) =0a(3) =2a(4) =4a(5) =13a(6) =40a(7) =130a(8) =432a(9) =1466a(10) =5056a(11) =17672a(12) =62460a(13) =222853a(14) =801592a(15) =2903626a(16) =10582816a(17) =38781310a(18) =142805056a(19) =528134764a(20) =1960825672a(21) =7305767602a(22) =27307800400a(23) =102371942932a(24) =384806950624