Number of Dyck paths of semilength n such that each positive level has exactly three peaks.

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =0a(5) =0a(6) =0a(7) =4a(8) =20a(9) =20a(10) =0a(11) =16a(12) =200a(13) =1120a(14) =3540a(15) =6864a(16) =9400a(17) =18240a(18) =82000a(19) =364256a(20) =1255040a(21) =3448400a(22) =8094400a(23) =18653984a(24) =50789120a(25) =166596240a(26) =565558400a(27) =1791310496a(28) =5202559520a(29) =14279014880