A343171 Irregular triangle read by rows: coefficients of polynomials xi_n.

1, 1, 3, 1, 11, 5, 57, 38, 5, 361, 302, 61, 2763, 2827, 845, 61, 24611, 29607, 11421, 1385, 250737, 347372, 165678, 30108, 1385, 2873041, 4501564, 2551326, 610444, 50521, 36581523, 63967093, 42044902, 12558738, 1578727, 50521

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Shi-Mei Ma, Qi Fang, Toufik Mansour, and Yeong-Nan Yeh, Alternating Eulerian polynomials and left peak polynomials, arXiv:2104.09374 [math.CO], 2021.

Example

Triangle begins:
    1;
    1;
    3,   1;
   11,   5;
   57,  38,  5;
  361, 302, 61;
  ...

Mathematica

xi[0][_] = 1;
xi[n_][x_] := xi[n, x] = (2n - 1 + (n-1) x) xi[n-1][x] - (1 + x)(4 + 2x)* xi[n-1]'[x];
Table[CoefficientList[xi[n][x], x], {n, 0, 10}] // Flatten (* Jean-François Alcover, Apr 21 2021 *)

Crossrefs

First column gives A001586.

Cf. A343170.

Sequence in context: A027446 A027516 A092808 * A113955 A110165 A111965

Adjacent sequences: A343168 A343169 A343170 * A343172 A343173 A343174

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 21 2021

Extensions

More terms from Jean-François Alcover, Apr 21 2021

Status

approved