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 A317165 Number of permutations of [n*(n+1)/2] with distinct lengths of increasing runs. 3
 1, 1, 5, 241, 188743, 2734858573, 892173483721887, 7469920269852025033699, 1841449549508718383891930251607, 14973026148724796464136435753195418043885, 4467880642339303169146446437381463615730321314015457, 53810913396105573079543194840166969124601447333276658546225661505 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = A317166(A000217(n)). a(n) >= A317273(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*(n+1)/2, 0\$2, {}): seq(a(n), n=0..8); CROSSREFS Cf. A000217, A246292, A317130, A317166, A317273. Sequence in context: A142732 A242625 A085115 * A327582 A144999 A215910 Adjacent sequences:  A317162 A317163 A317164 * A317166 A317167 A317168 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 23 2018 STATUS approved

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Last modified October 30 22:57 EDT 2020. Contains 338095 sequences. (Running on oeis4.)