Up-down permutations on [n] whose peaks have k rises.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =0a(5) =2a(6) =0a(7) =3a(8) =2a(9) =0a(10) =8a(11) =8a(12) =0a(13) =15a(14) =38a(15) =8a(16) =0a(17) =48a(18) =176a(19) =48a(20) =0a(21) =105a(22) =692a(23) =540a(24) =48a(25) =0a(26) =384a(27) =3584a(28) =3584a(29) =384