A215063 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, -18, 54, -45, 0, 15, -6, 1, 27, -126, 189, -105, 0, 21, -7, 1, -27, 216, -504, 504, -210, 0, 28, -8, 1, 0, -243, 972, -1512, 1134, -378, 0, 36, -9, 1, 81, 0, -1215

Offset: 0

Author

Peter Luschny, Aug 01 2012

Keywords

• sign
• tabl

Comments

Matrix inverse is A215062.

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] [-18, 54, -45, 0, 15, -6, 1]
[7] [27, -126, 189, -105, 0, 21, -7, 1]
[8] [-27, 216, -504, 504, -210, 0, 28, -8, 1]
[9] [0, -243, 972, -1512, 1134, -378, 0, 36, -9, 1]
		

Crossrefs

Cf. A215060, A215061, A215062, A215064, A215065.

Programs

Sage

def A215063_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)
A215063_triangle(12)