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A342314 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.

%I A342314 #8 Mar 19 2021 07:08:37
%S A342314 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 A342314 360,0,-198,65,544,0,-1680,0,1190,0,-455,129,0,6528,0,-8064,0,3696,0,
%U A342314 -1032,257,-15872,0,48960,0,-34272,0,10920,0,-2313,513,0,-238080,0,293760,0,-133056,0,30960,0,-5130,1025
%N A342314 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 A342314 Table starts:
%e A342314                              [0] 2
%e A342314                            [1] -2, 3
%e A342314                          [2] 0, -6, 5
%e A342314                        [3] 4, 0, -15, 9
%e A342314                      [4] 0, 24, 0, -36, 17
%e A342314                   [5] -32, 0, 100, 0, -85, 33
%e A342314                [6] 0, -288, 0, 360, 0, -198, 65
%e A342314            [7] 544, 0, -1680, 0, 1190, 0, -455, 129
%e A342314          [8] 0, 6528, 0, -8064, 0, 3696, 0, -1032, 257
%e A342314    [9] -15872, 0, 48960, 0, -34272, 0, 10920, 0, -2313, 513
%p A342314 CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
%p A342314 E := (n,x) -> 2^n*(euler(n, x/2) + euler(n, x));
%p A342314 seq(CoeffList(E(n, x)), n=0..9);
%Y A342314 Cf. A060096/A060097, A163982 (row sums).
%K A342314 sign,tabl
%O A342314 0,1
%A A342314 _Peter Luschny_, Mar 19 2021