A326485 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.

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, -24, 4, 17, 119, -84, -140, 70, 42, -28, 4, -31, 34, 119, -56, -70, 28, 14, -8, 1, -31, -279, 153, 357, -126, -126, 42, 18, -9, 1, 691, -620, -2790, 1020, 1785, -504, -420, 120, 45, -20, 2

Offset: 0

Author

Peter Luschny, Jul 12 2019

Keywords

• sign
• tabl

Comments

These are the coefficients of the generalized Euler polynomials (case m=2) with a different normalization. See A326480 for further comments.

Examples

			Triangle starts:
[0] [  1]
[1] [ -1,    1]
[2] [  1,   -4,   2]
[3] [  1,    3,  -6,    2]
[4] [ -1,    2,   3,   -4,    1]
[5] [ -1,   -5,   5,    5,   -5,    1]
[6] [ 17,  -24, -60,   40,   30,  -24,   4]
[7] [ 17,  119, -84, -140,   70,   42, -28,  4]
[8] [-31,   34, 119,  -56,  -70,   28,  14, -8,  1]
[9] [-31, -279, 153,  357, -126, -126,  42, 18, -9, 1]
		

Crossrefs

Cf. A326480, A050605.

Programs

Maple

E2n := proc(n) (4*exp(x*z))/(exp(z) + 1)^2;
series(%, z, 48); 2^A050605(n)*n!*coeff(%, z, n) end:
for n from 0 to 9 do PolynomialTools:-CoefficientList(E2n(n), x) od;