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A215062 Triangle read by rows, e.g.f. exp(x*(z+3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3). 5
1, 1, 1, 1, 2, 1, 0, 3, 3, 1, -3, 0, 6, 4, 1, -9, -15, 0, 10, 5, 1, 0, -54, -45, 0, 15, 6, 1, 99, 0, -189, -105, 0, 21, 7, 1, 477, 792, 0, -504, -210, 0, 28, 8, 1, 0, 4293, 3564, 0, -1134, -378, 0, 36, 9, 1, -11259, 0, 21465, 11880, 0, -2268 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..60.

FORMULA

Matrix inverse is A215063.

T(n,k) = A215064(n,k) - A215060(n,k) + [n==k]

EXAMPLE

[0] [1]

[1] [1, 1]

[2] [1, 2, 1]

[3] [0, 3, 3, 1]

[4] [-3, 0, 6, 4, 1]

[5] [-9, -15, 0, 10, 5, 1]

[6] [0, -54, -45, 0, 15, 6, 1]

[7] [99, 0, -189, -105, 0, 21, 7, 1]

[8] [477, 792, 0, -504, -210, 0, 28, 8, 1]

[9] [0, 4293, 3564, 0, -1134, -378, 0, 36, 9, 1]

MATHEMATICA

max = 11; f = Exp[x*(z + 3/2)]/((Exp[3*(x/2)] + 2*Cos[Sqrt[3]*(x/2)])/3); 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)

def A215062_triangle(dim): # See A215060 for function 'triangle'.

    var('x, z')

    f = exp(x*(z+3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)

    return triangle(f, dim)

A215062_triangle(12)

CROSSREFS

Cf. A215060, A215061, A215063, A215064, A215065.

Sequence in context: A079123 A121548 A180179 * A215063 A316781 A290733

Adjacent sequences:  A215059 A215060 A215061 * A215063 A215064 A215065

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Aug 01 2012

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)