cp's OEIS Frontend

A319029 Triangle read by rows: T(n,k) is the number of permutations pi of [n] such that pi has k descents and s(pi) avoids the patterns 132 and 321, where s is West's stack-sorting map (0 <= k <= n-1).

%I A319029 #14 Sep 14 2018 14:31:44
%S A319029 1,1,1,1,4,1,1,10,10,1,1,20,46,20,1,1,35,146,146,35,1,1,56,371,666,
%T A319029 371,56,1,1,84,812,2290,2290,812,84,1,1,120,1596,6504,10198,6504,1596,
%U A319029 120,1,1,165,2892,16080,36352,36352,16080,2892,165,1
%N A319029 Triangle read by rows: T(n,k) is the number of permutations pi of [n] such that pi has k descents and s(pi) avoids the patterns 132 and 321, where s is West's stack-sorting map (0 <= k <= n-1).
%C A319029 Row sums give A319028.
%H A319029 Colin Defant, <a href="https://arxiv.org/abs/1809.03123">Stack-sorting preimages of permutation classes</a>, arXiv:1809.03123 [math.CO], 2018.
%F A319029 T(n,k) = T(n, n-1-k).
%F A319029 G.f.: F(x,y) + x^3*y*((d/dx)F(x,y))^2, where F(x,y) = (1-x(y+1) - (1 - 2x(y+1) + x^2(y-1)^2)^(1/2))/(2xy) is the generating function of A001263.
%e A319029 Triangle begins:
%e A319029   1,
%e A319029   1,   1,
%e A319029   1,   4,   1,
%e A319029   1,  10,  10,   1,
%e A319029   1,  20,  46,  20,   1,
%e A319029   1,  35, 146, 146,  35,   1,
%e A319029   1,  56, 371, 666, 371,  56,   1,
%e A319029   ...
%t A319029 DeleteCases[Flatten[CoefficientList[Series[(1 - x (y + 1) - Sqrt[1 - 2 x (y + 1) + x^2 (y - 1)^2])/(2 x*y) + x^3*y (D[(1 - x (y + 1) - Sqrt[1 - 2 x (y + 1) + x^2 (y - 1)^2])/(2 x*y), x])^2, {x, 0, 10}], {x, y}]], 0]
%Y A319029 Cf. A319028, A001263.
%K A319029 easy,nonn,tabl
%O A319029 1,5
%A A319029 _Colin Defant_, Sep 10 2018