OFFSET
0,7
COMMENTS
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.
LINKS
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
EXAMPLE
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.
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Andrew Howroyd, Apr 24 2020
STATUS
approved