Number of Dyck paths of semilength n such that no level has more than four peaks.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =41a(6) =130a(7) =414a(8) =1365a(9) =4564a(10) =15491a(11) =53147a(12) =184014a(13) =641710a(14) =2251113a(15) =7937416a(16) =28108741a(17) =99903584a(18) =356181450a(19) =1273253851a(20) =4561936460a(21) =16377201916a(22) =58894487282a(23) =212108951615a(24) =764910126587