Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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