Number of permutations of {1..n} with all distinct lengths of maximal runs (increasing by 1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =5a(6) =23a(7) =25a(8) =43a(9) =63a(10) =345a(11) =365a(12) =665a(13) =949a(14) =1513a(15) =8175a(16) =9003a(17) =15929a(18) =23399a(19) =36949a(20) =51043a(21) =293715a(22) =314697a(23) =570353a(24) =826817a(25) =1318201a(26) =1810393a(27) =2766099a(28) =14180139a(29) =15600413