cp's OEIS Frontend

A227850 Number of Dyck paths of semilength n*(4*n+1) in which the run length sequence is a permutation of {1,...,4*n}.

%I A227850 #20 Apr 23 2016 11:16:08
%S A227850 1,4,1248,5401472,114070692352,7593330670240768
%N A227850 Number of Dyck paths of semilength n*(4*n+1) in which the run length sequence is a permutation of {1,...,4*n}.
%e A227850 a(1) = 4: UUDUUUDDDD (2134), UUUDUUDDDD (3124), UUUUDDUDDD (4213), UUUUDDDUDD (4312).
%p A227850 h:= proc(n, s) option remember;
%p A227850        `if`(n>add(sort([s[]], `>`)[i], i=1..(nops(s)+1)/2), 0,
%p A227850        add(g(n-i, s minus {i}), i=select(x-> x<=n, s)))
%p A227850     end:
%p A227850 g:= proc(n, s) option remember;
%p A227850        `if`(s={}, `if`(n=0, 1, 0), add(h(n+i, s minus {i}), i=s))
%p A227850     end:
%p A227850 a:= n-> g(0, {$1..4*n}):
%p A227850 seq(a(n), n=0..3);
%t A227850 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&]}] ];
%t A227850 g[n_, s_] := g[n, s] = If[s == {}, If[n == 0, 1, 0], Sum[h[n + i, s  ~Complement~ {i}], {i, s}]];
%t A227850 a[n_] := g[0, Range[4*n]];
%t A227850 Table[a[n], {n, 0, 4}] (* _Jean-François Alcover_, Apr 23 2016, translated from Maple *)
%Y A227850 Cf. A007742, A060005, A073410, A168238.
%K A227850 nonn,more
%O A227850 0,2
%A A227850 _David Scambler_ and _Alois P. Heinz_, Oct 31 2013