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A250266 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 10).

%I A250266 #12 Sep 03 2021 01:51:41
%S A250266 1,1,1,2,3,4,5,6,7,8,9,10,109,768,3627,13636,43665,123744,318223,
%T A250266 755802,1679581,3527140,70542781,878845662,7113969943,44573747024,
%U A250266 231938007625,1043938332476,4176060103827,15138650342428,50462774778029,156435448534980
%N A250266 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 10).
%H A250266 Alois P. Heinz, <a href="/A250266/b250266.txt">Table of n, a(n) for n = 0..500</a>
%p A250266 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A250266      `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 10)), j=1..u),
%p A250266                add(b(u+j-1, o-j, irem(t+1, 10)), j=1..o)))
%p A250266     end:
%p A250266 a:= n-> b(0, n, 0):
%p A250266 seq(a(n), n=0..35);
%t A250266 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, 10]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 10]], {j, 1, o}]]];
%t A250266 a[n_] := b[0, n, 0];
%t A250266 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jul 22 2019, after _Alois P. Heinz_ *)
%Y A250266 Column k=10 of A250261.
%K A250266 nonn
%O A250266 0,4
%A A250266 _Alois P. Heinz_, Nov 15 2014