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A177524 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down.

%I A177524 #17 Apr 20 2022 10:31:29
%S A177524 1,1,2,6,24,120,715,4970,39480,352800,3502800,38255900,455795100,
%T A177524 5883052500,81774966000,1217871018000,19346879737625,326549862671250,
%U A177524 5835951345093750,110091785625495000,2186122850020215000,45580964489553559375,995625115672520581250
%N A177524 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down.
%H A177524 Alois P. Heinz, <a href="/A177524/b177524.txt">Table of n, a(n) for n = 0..170</a>
%F A177524 a(n) ~ c * d^n * n!, where d = 0.9928637443921790380857377558103269268777241137790934589694993..., c = 1.0369478195304845650491426260146999487076420703190374702807322... . - _Vaclav Kotesovec_, Aug 29 2014
%p A177524 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
%p A177524       add(b(u-j, o+j-1, `if`(t=1, 1, t+1)), j=1..u)+
%p A177524       add(b(u+j-1, o-j, 2), j=1..o)))
%p A177524     end:
%p A177524 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177524 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177524 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o == 0, 1,
%t A177524      Sum[b[u - j, o + j - 1, If[t == 1, 1, t + 1]], {j, 1, u}] +
%t A177524      Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
%t A177524 a[n_] := If[n == 0, 1, Sum[b[j - 1, n - j, 1], {j, 1, n}]];
%t A177524 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 20 2022, after _Alois P. Heinz_ *)
%Y A177524 Columns k=16,30 of A242784.
%K A177524 nonn
%O A177524 0,3
%A A177524 _R. H. Hardin_, May 10 2010
%E A177524 a(17)-a(22) from _Alois P. Heinz_, Oct 20 2013