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 A227850 Number of Dyck paths of semilength n*(4*n+1) in which the run length sequence is a permutation of {1,...,4*n}. 3
 1, 4, 1248, 5401472, 114070692352, 7593330670240768 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE a(1) = 4: UUDUUUDDDD (2134), UUUDUUDDDD (3124), UUUUDDUDDD (4213), UUUUDDDUDD (4312). MAPLE h:= proc(n, s) option remember;        `if`(n>add(sort([s[]], `>`)[i], i=1..(nops(s)+1)/2), 0,        add(g(n-i, s minus {i}), i=select(x-> x<=n, s)))     end: g:= proc(n, s) option remember;        `if`(s={}, `if`(n=0, 1, 0), add(h(n+i, s minus {i}), i=s))     end: a:= n-> g(0, {\$1..4*n}): seq(a(n), n=0..3); MATHEMATICA h[n_, s_] := h[n, s] = If[n > Sum[Sort[s, Greater][[i]], {i, 1, (Length[s] + 1)/2}], 0, Sum[g[n - i, s ~Complement~ {i}], {i, Select[s, # <= n&]}] ]; g[n_, s_] := g[n, s] = If[s == {}, If[n == 0, 1, 0], Sum[h[n + i, s  ~Complement~ {i}], {i, s}]]; a[n_] := g[0, Range[4*n]]; Table[a[n], {n, 0, 4}] (* Jean-François Alcover, Apr 23 2016, translated from Maple *) CROSSREFS Cf. A007742, A060005, A073410, A168238. Sequence in context: A253168 A160004 A324299 * A079711 A283260 A217601 Adjacent sequences:  A227847 A227848 A227849 * A227851 A227852 A227853 KEYWORD nonn,more AUTHOR David Scambler and Alois P. Heinz, Oct 31 2013 STATUS approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)