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A215064 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). 7
1, 1, 1, 1, 2, 1, -1, 3, 3, 1, -3, -4, 6, 4, 1, -9, -15, -10, 10, 5, 1, 19, -54, -45, -20, 15, 6, 1, 99, 133, -189, -105, -35, 21, 7, 1, 477, 792, 532, -504, -210, -56, 28, 8, 1, -1513, 4293, 3564, 1596, -1134, -378, -84, 36, 9, 1, -11259 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..55.

FORMULA

Matrix inverse is A215065.

T(n,k) = A215060(n,k) + A215062(n,k) - [n==k].

|T(n,0)| = A178963(n).

|T(3*n,0)| = A002115(n).

EXAMPLE

[0] [1]

[1] [1, 1]

[2] [1, 2, 1]

[3] [-1, 3, 3, 1]

[4] [-3, -4, 6, 4, 1]

[5] [-9, -15, -10, 10, 5, 1]

[6] [19, -54, -45, -20, 15, 6, 1]

[7] [99, 133, -189, -105, -35, 21, 7, 1]

[8] [477, 792, 532, -504, -210, -56, 28, 8, 1]

[9] [-1513, 4293, 3564, 1596, -1134, -378, -84, 36, 9, 1]

MATHEMATICA

max = 11; 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-Fran├žois Alcover, Jul 29 2013 *)

PROG

(Sage) # uses[triangle from A215060]

def A215064_triangle(dim):

    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)

A215064_triangle(12)

CROSSREFS

Cf. A215060, A215061, A215062, A215063, A215065.

Sequence in context: A297359 A338291 A029264 * A124054 A299208 A334187

Adjacent sequences:  A215061 A215062 A215063 * A215065 A215066 A215067

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Aug 01 2012

STATUS

approved

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Last modified June 20 03:33 EDT 2021. Contains 345157 sequences. (Running on oeis4.)