0,7

The polynomials are scaled by a factor of n!*2^n to ensure integer coefficients. When evaluated at x = k, they give the number of non-isomorphic k-colorings of the n-hypercube graph under the automorphism group of the graph. The size of the automorphism group is n!*2^n. Colors may not be interchanged.

Andrew Howroyd, Table of n, a(n) for n = 0..68 (rows 0..5)

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Eric Weisstein's World of Mathematics, Hypercube Graph

Triangle begins:

0 | 1, 0;

1 | 1, -1, 0;

2 | 1, -2, 3, -2, 0;

3 | 1, -12, 72, -256, 579, -812, 644, -216, 0;

...

The corresponding polynomials are:

x;

(x^2 - x)/(1!*2^1);

(x^4 - 2*x^3 + 3*x^2 - 2*x)/(2!*2^2);

(x^8 - 12*x^7 + 72*x^6 - 256*x^5 + 579*x^4 - 812*x^3 + 644*x^2 - 216*x)/(3!*2^3);

...

The polynomial (x^4 - 2*x^3 + 3*x^2 - 2*x)/(2!*2^2) gives A002817 when evaluated at integer values of x.

Cf. A002817, A334159, A334248, A334356, A334357.

Sequence in context: A247490 A002120 A021435 * A226556 A007325 A247920

Adjacent sequences: A334355 A334356 A334357 * A334359 A334360 A334361

sign,tabf

Andrew Howroyd, Apr 24 2020

approved