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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, 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
0,5
COMMENTS
These are the coefficients of the generalized Euler polynomials (case m=2) with a different normalization. See A326480 for further comments.
EXAMPLE
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]
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;
CROSSREFS
Sequence in context: A375119 A010311 A346972 * A023528 A236308 A105698
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Jul 12 2019
STATUS
approved