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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.
1
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
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
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;
...
CROSSREFS
Row sums are A001879(n-2).
Sequence in context: A248978 A143461 A066808 * A033918 A136467 A079188
KEYWORD
nonn,tabf
AUTHOR
Jose Bastidas, Jun 28 2023
STATUS
approved