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A342315 T(n, k) = [x^k] 2^n*(Euler(n, x) - Euler(n, x/2)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.

%I A342315 #9 Mar 19 2021 07:08:01
%S A342315 0,0,1,0,-2,3,0,0,-9,7,0,8,0,-28,15,0,0,60,0,-75,31,0,-96,0,280,0,
%T A342315 -186,63,0,0,-1008,0,1050,0,-441,127,0,2176,0,-6272,0,3472,0,-1016,
%U A342315 255,0,0,29376,0,-30240,0,10584,0,-2295,511,0,-79360,0,228480,0,-124992,0,30480,0,-5110,1023
%N A342315 T(n, k) = [x^k] 2^n*(Euler(n, x) - Euler(n, x/2)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.
%e A342315 Table starts:
%e A342315                             [0] 0
%e A342315                            [1] 0, 1
%e A342315                          [2] 0, -2, 3
%e A342315                         [3] 0, 0, -9, 7
%e A342315                      [4] 0, 8, 0, -28, 15
%e A342315                    [5] 0, 0, 60, 0, -75, 31
%e A342315                 [6] 0, -96, 0, 280, 0, -186, 63
%e A342315             [7] 0, 0, -1008, 0, 1050, 0, -441, 127
%e A342315          [8] 0, 2176, 0, -6272, 0, 3472, 0, -1016, 255
%e A342315       [9] 0, 0, 29376, 0, -30240, 0, 10584, 0, -2295, 511
%p A342315 CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
%p A342315 E := (n, x) -> 2^n*(euler(n, x) - euler(n, x/2));
%p A342315 0,seq(CoeffList(E(n, x)), n = 0..10);
%Y A342315 Cf. A060096/A060097, A163747 (row sums).
%K A342315 sign,tabl
%O A342315 0,5
%A A342315 _Peter Luschny_, Mar 19 2021