A360605 The polygonal polynomials evaluated at x = -1/2 and normalized with (-2)^n.

0, 1, 0, 1, 0, -3, 8, -31, 72, -195, 448, -1071, 2416, -5475, 12120, -26719, 58232, -126243, 271824, -582575, 1242720, -2640899, 5592360, -11806239, 24855080, -52195843, 109362528, -228667311, 477218512, -994205475, 2067947128, -4294967391, 8908080216

Offset

0,6

Comments

The coefficients of the polygonal polynomials are the antidiagonals of A139600.

Links

Table of n, a(n) for n=0..32.

Formula

a(n) = (-2)^n * Sum_{k=0..n} A139600(n, k) * (-2)^(-k).

a(n) = [x^n] x*(4*x^2 - x - 1) / ((2*x + 1)^2*(x - 1)^3).

a(n) = (4 - n)*(3*n + 2 + (-2)^(n + 1)) / 27.

Maple

a := n -> (1/27)*(4-n)*(3*n + 2 + (-2)^(n + 1)):
seq(a(n), n = 0..32);

Crossrefs

Cf. A139600, A360606.

Sequence in context: A145776 A066165 A323775 * A119838 A148889 A148890

Adjacent sequences: A360602 A360603 A360604 * A360606 A360607 A360608

Keyword

sign

Author

Peter Luschny, Feb 21 2023

Status

approved