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 A317166 Number of permutations of [n] with distinct lengths of increasing runs. 3
 1, 1, 1, 5, 7, 27, 241, 505, 1975, 10241, 188743, 460545, 2323679, 10836141, 85023209, 2734858573, 8010483015, 45714797671, 243112435345, 1632532938001, 15831051353773, 892173483721887, 2978105991739613, 19855526019022967, 113487352591708591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..66 FORMULA a(A000217(n)) = A317165(n). MAPLE g:= (n, s)-> `if`(n in s, 0, 1): b:= proc(u, o, t, s) option remember; `if`(u+o=0, g(t, s),       `if`(g(t, s)=1, add(b(u-j, o+j-1, 1, s union {t})        , j=1..u), 0)+ add(b(u+j-1, o-j, t+1, s), j=1..o))     end: a:= n-> b(n, 0\$2, {}): seq(a(n), n=0..24); CROSSREFS Cf. A000217, A007838, A317165. Sequence in context: A029668 A144392 A268701 * A126888 A185302 A179305 Adjacent sequences:  A317163 A317164 A317165 * A317167 A317168 A317169 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 23 2018 STATUS approved

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Last modified October 27 19:26 EDT 2020. Contains 338035 sequences. (Running on oeis4.)