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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.

Original entry on oeis.org

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

Author

Jose Bastidas, Jun 28 2023

Keywords

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).

Examples

			    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).