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%I #18 Dec 22 2020 03:54:00
%S 1,1,1,1,1,1,1,6,21,56,126,252,2562,14442,59487,199627,578005,8330800,
%T 65056960,363823800,1628423880,6190034016,115452938151,1152005977431,
%U 8137667253101,45527993728141,214265281290061,4904624749585886,59578069604921361
%N Number of 5 up, 5 down permutations of [n].
%C Limit n->infinity (a(n)/n!)^(1/n) = 0.337596001995... . - _Vaclav Kotesovec_, Sep 06 2014
%H Alois P. Heinz, <a href="/A229886/b229886.txt">Table of n, a(n) for n = 0..545</a>
%e a(6) = 1: 123456.
%e a(7) = 6: 1234576, 1234675, 1235674, 1245673, 1345672, 2345671.
%e a(8) = 21: 12345876, 12346875, 12347865, 12356874, 12357864, 12367854, 12456873, 12457863, 12467853, 12567843, 13456872, 13457862, 13467852, 13567842, 14567832, 23456871, 23457861, 23467851, 23567841, 24567831, 34567821.
%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=5,
%p b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
%p end:
%p a:= n-> b(0, n, 0):
%p seq(a(n), n=0..35);
%t b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == 5, b[o - j, u + j - 1, 1], b[u + j - 1, o - j, t + 1]], {j, 1, o}]];
%t a[n_] := b[0, n, 0];
%t a /@ Range[0, 35] (* _Jean-François Alcover_, Dec 22 2020, after _Alois P. Heinz_ *)
%Y Column k=5 of A229892.
%K nonn,eigen
%O 0,8
%A _Alois P. Heinz_, Oct 02 2013
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