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A334358 Irregular triangle read by rows: row n gives scaled coefficients of the chromatic polynomial corresponding to colorings of the n-hypercube graph up to automorphism, highest powers first, 0 <= k <= 2^n.

%I A334358 #11 Feb 16 2025 08:34:00
%S A334358 1,0,1,-1,0,1,-2,3,-2,0,1,-12,72,-256,579,-812,644,-216,0,1,-32,496,
%T A334358 -4936,35276,-191840,820328,-2808636,7759343,-17276144,30675244,
%U A334358 -42494732,44214736,-32375904,14772272,-3125472,0,1,-80,3160,-82080,1575420,-23805776,294640000
%N A334358 Irregular triangle read by rows: row n gives scaled coefficients of the chromatic polynomial corresponding to colorings of the n-hypercube graph up to automorphism, highest powers first, 0 <= k <= 2^n.
%C A334358 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.
%H A334358 Andrew Howroyd, <a href="/A334358/b334358.txt">Table of n, a(n) for n = 0..68</a> (rows 0..5)
%H A334358 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A334358 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%e A334358 Triangle begins:
%e A334358   0 | 1, 0;
%e A334358   1 | 1, -1, 0;
%e A334358   2 | 1, -2, 3, -2, 0;
%e A334358   3 | 1, -12, 72, -256, 579, -812, 644, -216, 0;
%e A334358   ...
%e A334358 The corresponding polynomials are:
%e A334358   x;
%e A334358   (x^2 - x)/(1!*2^1);
%e A334358   (x^4 - 2*x^3 + 3*x^2 - 2*x)/(2!*2^2);
%e A334358   (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);
%e A334358   ...
%e A334358 The polynomial (x^4 - 2*x^3 + 3*x^2 - 2*x)/(2!*2^2) gives A002817 when evaluated at integer values of x.
%Y A334358 Cf. A002817, A334159, A334248, A334356, A334357.
%K A334358 sign,tabf
%O A334358 0,7
%A A334358 _Andrew Howroyd_, Apr 24 2020