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
Examples
Triangle begins:
1;
1;
3, 1;
11, 5;
57, 38, 5;
361, 302, 61;
...
Links
- Shi-Mei Ma, Qi Fang, Toufik Mansour, and Yeong-Nan Yeh, Alternating Eulerian polynomials and left peak polynomials, arXiv:2104.09374 [math.CO], 2021.
Programs
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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 *)
Extensions
More terms from Jean-François Alcover, Apr 21 2021