A215065 Triangle read by rows, e.g.f. exp(x*z)/((exp(x/2)+exp(x*3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)-1).

1, -1, 1, 1, -2, 1, 1, 3, -3, 1, -11, 4, 6, -4, 1, 49, -55, 10, 10, -5, 1, -137, 294, -165, 20, 15, -6, 1, -127, -959, 1029, -385, 35, 21, -7, 1, 5573, -1016, -3836, 2744, -770, 56, 28, -8, 1, -50399, 50157, -4572, -11508, 6174, -1386, 84

Offset

0,5

Comments

Matrix inverse is A215064.

Links

Table of n, a(n) for n=0..51.

Example

[0] [1]
[1] [-1, 1]
[2] [1, -2, 1]
[3] [1, 3, -3, 1]
[4] [-11, 4, 6, -4, 1]
[5] [49, -55, 10, 10, -5, 1]
[6] [-137, 294, -165, 20, 15, -6, 1]
[7] [-127, -959, 1029, -385, 35, 21, -7, 1]
[8] [5573, -1016, -3836, 2744, -770, 56, 28, -8, 1]
[9] [-50399, 50157, -4572, -11508, 6174, -1386, 84, 36, -9, 1]

Mathematica

max = 10; f = Exp[x*z]/((Exp[x/2] + Exp[x*(3/2)])/((Exp[3*(x/2)] + 2*Cos[Sqrt[3]*(x/2)])/3) - 1); coes = CoefficientList[ Series[f, {x, 0, max}, {z, 0, max}], {x, z}]; Table[ coes[[n, k]]*(n - 1)!, {n, 1, max}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 29 2013 *)

Prog

(Sage)
def A215065_triangle(dim): # See A215060 for function 'triangle'.
    var('x, z')
    f = exp(x*z)/((exp(x/2)+exp(x*3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)-1)
    return triangle(f, dim)
A215065_triangle(12)

Crossrefs

Cf. A215060, A215061, A215062, A215063, A215064.

Sequence in context: A010356 A100640 A242779 * A175424 A144401 A034929

Adjacent sequences: A215062 A215063 A215064 * A215066 A215067 A215068

Keyword

sign,tabl

Author

Peter Luschny, Aug 01 2012

Status

approved