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A363935 Triangle of coefficients of the primitive Eulerian polynomials of type D T(n,k) (n >= 2, 1 <= k <= n) read by rows.

%I A363935 #25 Jul 17 2023 01:18:58
%S A363935 0,1,1,4,1,4,20,20,1,11,116,216,76,1,26,632,2072,1732,262,1,57,3158,
%T A363935 18404,28064,11824,862,1,120,14800,151104,386640,317200,73320,2760,1,
%U A363935 247,66424,1158040,4777264,6608800,3169168,427576,8680,1
%N A363935 Triangle of coefficients of the primitive Eulerian polynomials of type D T(n,k) (n >= 2, 1 <= k <= n) read by rows.
%C A363935 Row n counts even signed permutations w in D_n such that (i.) w(1) != -n and (ii.) all right-to-left maxima of |w| are negative in w, by their type D descent number. For example, T(3,2) = 4 counts the signed permutations (1,-3,-2), (-2,1,-3), (2,-1,-3), (2,-3,-1).
%H A363935 Jose Bastidas, <a href="/A363935/b363935.txt">Table of n, a(n) for n = 2..1225</a>
%H A363935 J. Bastidas, C. Hohlweg and F. Saliola, <a href="https://arxiv.org/abs/2306.15556">The Primitive Eulerian polynomial</a>, arXiv:2306.15556 [math.CO], 2023. Table 3.
%e A363935     0,     1;
%e A363935     1,     4,      1;
%e A363935     4,    20,     20,      1;
%e A363935    11,   116,    216,     76,      1;
%e A363935    26,   632,   2072,   1732,    262,     1;
%e A363935    57,  3158,  18404,  28064,  11824,   862,    1;
%e A363935   120, 14800, 151104, 386640, 317200, 73320, 2760, 1;
%e A363935   ...
%Y A363935 Row sums are A001879(n-2).
%K A363935 nonn,tabf
%O A363935 2,4
%A A363935 _Jose Bastidas_, Jun 28 2023