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A343171 Irregular triangle read by rows: coefficients of polynomials xi_n. 1

%I

%S 1,1,3,1,11,5,57,38,5,361,302,61,2763,2827,845,61,24611,29607,11421,

%T 1385,250737,347372,165678,30108,1385,2873041,4501564,2551326,610444,

%U 50521,36581523,63967093,42044902,12558738,1578727,50521

%N Irregular triangle read by rows: coefficients of polynomials xi_n.

%H 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 Triangle begins:

%e 1;

%e 1;

%e 3, 1;

%e 11, 5;

%e 57, 38, 5;

%e 361, 302, 61;

%e ...

%t xi[0][_] = 1;

%t xi[n_][x_] := xi[n, x] = (2n - 1 + (n-1) x) xi[n-1][x] - (1 + x)(4 + 2x)* xi[n-1]'[x];

%t Table[CoefficientList[xi[n][x], x], {n, 0, 10}] // Flatten (* _Jean-Fran├žois Alcover_, Apr 21 2021 *)

%Y First column gives A001586.

%Y Cf. A343170.

%K nonn,tabf

%O 0,3

%A _N. J. A. Sloane_, Apr 21 2021

%E More terms from _Jean-Fran├žois Alcover_, Apr 21 2021

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)