A363935 - OEIS

A363935

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

0, 1, 1, 4, 1, 4, 20, 20, 1, 11, 116, 216, 76, 1, 26, 632, 2072, 1732, 262, 1, 57, 3158, 18404, 28064, 11824, 862, 1, 120, 14800, 151104, 386640, 317200, 73320, 2760, 1, 247, 66424, 1158040, 4777264, 6608800, 3169168, 427576, 8680, 1

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OFFSET

2,4

COMMENTS

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).

LINKS

Jose Bastidas, Table of n, a(n) for n = 2..1225

J. Bastidas, C. Hohlweg and F. Saliola, The Primitive Eulerian polynomial, arXiv:2306.15556 [math.CO], 2023. Table 3.

EXAMPLE

0, 1;

1, 4, 1;

4, 20, 20, 1;

11, 116, 216, 76, 1;

26, 632, 2072, 1732, 262, 1;

57, 3158, 18404, 28064, 11824, 862, 1;

120, 14800, 151104, 386640, 317200, 73320, 2760, 1;

...