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%I #10 Jul 13 2019 00:49:41
%S 1,-1,1,1,-4,2,1,3,-6,2,-1,2,3,-4,1,-1,-5,5,5,-5,1,17,-24,-60,40,30,
%T -24,4,17,119,-84,-140,70,42,-28,4,-31,34,119,-56,-70,28,14,-8,1,-31,
%U -279,153,357,-126,-126,42,18,-9,1,691,-620,-2790,1020,1785,-504,-420,120,45,-20,2
%N T(n, k) = 2^A050605(n) * n! * [x^k] [z^n] (4*exp(x*z))/(exp(z) + 1)^2, triangle read by rows, for 0 <= k <= n.
%C These are the coefficients of the generalized Euler polynomials (case m=2) with a different normalization. See A326480 for further comments.
%e Triangle starts:
%e [0] [ 1]
%e [1] [ -1, 1]
%e [2] [ 1, -4, 2]
%e [3] [ 1, 3, -6, 2]
%e [4] [ -1, 2, 3, -4, 1]
%e [5] [ -1, -5, 5, 5, -5, 1]
%e [6] [ 17, -24, -60, 40, 30, -24, 4]
%e [7] [ 17, 119, -84, -140, 70, 42, -28, 4]
%e [8] [-31, 34, 119, -56, -70, 28, 14, -8, 1]
%e [9] [-31, -279, 153, 357, -126, -126, 42, 18, -9, 1]
%p E2n := proc(n) (4*exp(x*z))/(exp(z) + 1)^2;
%p series(%, z, 48); 2^A050605(n)*n!*coeff(%, z, n) end:
%p for n from 0 to 9 do PolynomialTools:-CoefficientList(E2n(n), x) od;
%Y Cf. A326480, A050605.
%K sign,tabl
%O 0,5
%A _Peter Luschny_, Jul 12 2019
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