OFFSET
0,2
FORMULA
EXAMPLE
[0] [ 1]
[1] [ 2, -2]
[2] [ 6, -8, 4]
[3] [ 20, -36, 24, -8]
[4] [ 72, -160, 144, -64, 16]
[5] [ 272, -720, 800, -480, 160, -32]
[6] [ 1056, -3264, 4320, -3200, 1440, -384, 64]
[7] [ 4160, -14784, 22848, -20160, 11200, -4032, 896, -128]
[8] [16512, -66560, 118272, -121856, 80640, -35840, 10752, -2048, 256]
[9] [65792, -297216, 599040, -709632, 548352, -290304, 107520, -27648, 4608, -512]
MAPLE
IE2 := proc(n) (exp(z) + 1)^2/(4*exp(x*z));
series(%, z, 48); 2^n*n!*coeff(%, z, n) end:
for n from 0 to 9 do PolynomialTools:-CoefficientList(IE2(n), x) od;
MATHEMATICA
T[n_, k_] := 2^n n! SeriesCoefficient[(E^z + 1)^2/(4 E^(x z)), {x, 0, k}, {z, 0, n}]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 21 2019 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Jul 12 2019
STATUS
approved