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A343170 Triangle read by rows: coefficients of type B alternating Eulerian polynomials.

%I A343170 #16 Aug 25 2021 16:27:48
%S A343170 1,1,1,3,2,3,11,13,13,11,57,76,118,76,57,361,597,962,962,597,361,2763,
%T A343170 5270,9733,10548,9733,5270,2763,24611,53849,107427,136673,136673,
%U A343170 107427,53849,24611,250737,616408,1334556,1875432,2167654,1875432,1334556,616408,250737
%N A343170 Triangle read by rows: coefficients of type B alternating Eulerian polynomials.
%H A343170 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 A343170 Triangle begins:
%e A343170    1;
%e A343170    1,  1;
%e A343170    3,  2,   3;
%e A343170   11, 13,  13, 11;
%e A343170   57, 76, 118, 76, 57;
%e A343170   ...
%t A343170 Bhat[0][_] = 1; Bhat[1][x_] := 1 + x;
%t A343170 Bhat[n_][x_] := Bhat[n][x] = (n + x + (n-1) x^2) Bhat[n - 1][x] + (1 - x)* (1 + x^2) Bhat[n-1]'[x];
%t A343170 Table[CoefficientList[Bhat[n][x], x], {n, 0, 8}] // Flatten (* _Jean-François Alcover_, Apr 21 2021 *)
%Y A343170 Cf. A145876, A343171.
%K A343170 nonn,tabl
%O A343170 0,4
%A A343170 _N. J. A. Sloane_, Apr 21 2021
%E A343170 More terms from _Jean-François Alcover_, Apr 21 2021