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

%I A343171 #17 Apr 21 2021 23:52:28
%S A343171 1,1,3,1,11,5,57,38,5,361,302,61,2763,2827,845,61,24611,29607,11421,
%T A343171 1385,250737,347372,165678,30108,1385,2873041,4501564,2551326,610444,
%U A343171 50521,36581523,63967093,42044902,12558738,1578727,50521
%N A343171 Irregular triangle read by rows: coefficients of polynomials xi_n.
%H A343171 Shi-Mei Ma, Qi Fang, Toufik Mansour, and Yeong-Nan Yeh, <a href="https://arxiv.org/abs/2104.09374">Alternating Eulerian polynomials and left peak polynomials</a>, arXiv:2104.09374 [math.CO], 2021.
%e A343171 Triangle begins:
%e A343171     1;
%e A343171     1;
%e A343171     3,   1;
%e A343171    11,   5;
%e A343171    57,  38,  5;
%e A343171   361, 302, 61;
%e A343171   ...
%t A343171 xi[0][_] = 1;
%t A343171 xi[n_][x_] := xi[n, x] = (2n - 1 + (n-1) x) xi[n-1][x] - (1 + x)(4 + 2x)* xi[n-1]'[x];
%t A343171 Table[CoefficientList[xi[n][x], x], {n, 0, 10}] // Flatten (* _Jean-François Alcover_, Apr 21 2021 *)
%Y A343171 First column gives A001586.
%Y A343171 Cf. A343170.
%K A343171 nonn,tabf
%O A343171 0,3
%A A343171 _N. J. A. Sloane_, Apr 21 2021
%E A343171 More terms from _Jean-François Alcover_, Apr 21 2021