A215062 Triangle read by rows, e.g.f. exp(x*(z+3/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3).

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

Offset: 0

Author

Peter Luschny, Aug 01 2012

Keywords

• sign
• tabl

Examples

			[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]
		

Crossrefs

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

Programs

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-François Alcover, Jul 29 2013 *)

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)

Formula

Matrix inverse is A215063.

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