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A250265 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 9).

%I A250265 #12 Sep 03 2021 01:51:37
%S A250265 1,1,1,2,3,4,5,6,7,8,9,89,583,2562,8996,27013,72057,175016,393805,
%T A250265 831384,14964895,171416216,1274511567,7351608748,35319494255,
%U A250265 147208687584,546836589610,1845658907261,5742168041637,149870423643695,2452427105334001,25693720399771170
%N A250265 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 9).
%H A250265 Alois P. Heinz, <a href="/A250265/b250265.txt">Table of n, a(n) for n = 0..500</a>
%p A250265 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A250265      `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 9)), j=1..u),
%p A250265                add(b(u+j-1, o-j, irem(t+1, 9)), j=1..o)))
%p A250265     end:
%p A250265 a:= n-> b(0, n, 0):
%p A250265 seq(a(n), n=0..35);
%t A250265 b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t == 1, Sum[b[u - j, o + j - 1, Mod[t + 1, 9]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 9]], {j, 1, o}]]];
%t A250265 a[n_] := b[0, n, 0];
%t A250265 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jul 22 2019, after _Alois P. Heinz_ *)
%Y A250265 Column k=9 of A250261.
%K A250265 nonn
%O A250265 0,4
%A A250265 _Alois P. Heinz_, Nov 15 2014