Number of Dyck paths of semilength n such that all positive levels have the same number of peaks.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =1a(5) =8a(6) =13a(7) =13a(8) =54a(9) =132a(10) =280a(11) =547a(12) =1219a(13) =3904a(14) =11107a(15) =25082a(16) =53777a(17) =137751a(18) =419831a(19) =1257599a(20) =3453557a(21) =8911341a(22) =22636845a(23) =59890162a(24) =172264224a(25) =529706648a(26) =1630328686a(27) =4765347773a(28) =13125989799a(29) =35253234315