%I #8 Mar 19 2021 07:08:37
%S 2,-2,3,0,-6,5,4,0,-15,9,0,24,0,-36,17,-32,0,100,0,-85,33,0,-288,0,
%T 360,0,-198,65,544,0,-1680,0,1190,0,-455,129,0,6528,0,-8064,0,3696,0,
%U -1032,257,-15872,0,48960,0,-34272,0,10920,0,-2313,513,0,-238080,0,293760,0,-133056,0,30960,0,-5130,1025
%N T(n, k) = [x^k] 2^n*(Euler(n, x/2) + Euler(n, x)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.
%e Table starts:
%e [0] 2
%e [1] -2, 3
%e [2] 0, -6, 5
%e [3] 4, 0, -15, 9
%e [4] 0, 24, 0, -36, 17
%e [5] -32, 0, 100, 0, -85, 33
%e [6] 0, -288, 0, 360, 0, -198, 65
%e [7] 544, 0, -1680, 0, 1190, 0, -455, 129
%e [8] 0, 6528, 0, -8064, 0, 3696, 0, -1032, 257
%e [9] -15872, 0, 48960, 0, -34272, 0, 10920, 0, -2313, 513
%p CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
%p E := (n,x) -> 2^n*(euler(n, x/2) + euler(n, x));
%p seq(CoeffList(E(n, x)), n=0..9);
%Y Cf. A060096/A060097, A163982 (row sums).
%K sign,tabl
%O 0,1
%A _Peter Luschny_, Mar 19 2021