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%I #19 Dec 21 2020 02:33:25
%S 1,1,1,1,1,1,5,15,35,70,574,2674,9274,26599,305747,1944033,8995805,
%T 33757360,498851248,4017418768,23236611280,107709888805,1945409895065,
%U 18965460022971,131635127294783,726401013530416,15505381392117616,177447751441161616
%N Number of 4 up, 4 down permutations of [n].
%C Limit n->infinity (a(n)/n!)^(1/n) = 0.38605986196... . - _Vaclav Kotesovec_, Sep 06 2014
%H Alois P. Heinz, <a href="/A229885/b229885.txt">Table of n, a(n) for n = 0..200</a>
%e a(5) = 1: 12345.
%e a(6) = 5: 123465, 123564, 124563, 134562, 234561.
%e a(7) = 15: 1234765, 1235764, 1236754, 1245763, 1246753, 1256743, 1345762, 1346752, 1356742, 1456732, 2345761, 2346751, 2356741, 2456731, 3456721.
%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=4,
%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..30);
%t b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == 4, 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, 30] (* _Jean-François Alcover_, Dec 21 2020, after _Alois P. Heinz_ *)
%Y Column k=4 of A229892.
%Y Cf. A005983.
%K nonn,eigen
%O 0,7
%A _Alois P. Heinz_, Oct 02 2013
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