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

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;
  ...

Crossrefs

Row sums are A001879(n-2).

Sequence in context: A248978 A143461 A066808 * A033918 A136467 A079188

Adjacent sequences: A363932 A363933 A363934 * A363936 A363937 A363938

Keyword

nonn,tabf

Author

Jose Bastidas, Jun 28 2023

Status

approved