Number of peaks at even level in all symmetric Dyck paths of semilength n+2.

Terms

a(0) =1a(1) =2a(2) =7a(3) =12a(4) =34a(5) =60a(6) =155a(7) =280a(8) =686a(9) =1260a(10) =2982a(11) =5544a(12) =12804a(13) =24024a(14) =54483a(15) =102960a(16) =230230a(17) =437580a(18) =967538a(19) =1847560a(20) =4047836a(21) =7759752a(22) =16871582a(23) =32449872a(24) =70100044a(25) =135207800a(26) =290473900a(27) =561632400a(28) =1200823560a(29) =2326762800