Number of 1 up, 3 down, 5 up, 7 down, ... permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =19a(7) =55a(8) =125a(9) =245a(10) =434a(11) =4060a(12) =21186a(13) =81212a(14) =254813a(15) =692678a(16) =1688555a(17) =3776432a(18) =60101767a(19) =511650887a(20) =3089821383a(21) =14824989723a(22) =60057570858a(23) =213302293918a(24) =681247718668