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%I #14 Feb 28 2021 19:59:07
%S 0,1,0,2,0,0,3,2,0,0,4,6,2,0,0,5,12,18,2,0,0,6,20,84,114,2,0,0,7,30,
%T 260,2652,2970,2,0,0,8,42,630,29660,1321860,1185282,2,0,0,9,56,1302,
%U 198030,187430900,130253748108,100301050602,2,0,0,10,72,2408,932862,10199069190,2157531034816940
%N Table read by antidiagonals upwards: T(n,k) is the number of n-colorings of the vertices of the k-dimensional hypercube such that no two adjacent vertices have the same color. n >= 0, k >=0.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%F T(n,k) = Sum_{i=0..2^k} A334278(k,i)*n^i.
%e Table begins:
%e n\k| 0 1 2 3 4 5
%e ---+-----------------------------------------------------------------------
%e 0 | 0 0 0 0 0 0
%e 1 | 1 0 0 0 0 0
%e 2 | 2 2 2 2 2 2
%e 3 | 3 6 18 114 2970 1185282
%e 4 | 4 12 84 2652 1321860 130253748108
%e 5 | 5 20 260 29660 187430900 2157531034816940
%e 6 | 6 30 630 198030 10199069190 7905235551766437150
%e 7 | 7 42 1302 932862 269591166222 7365707045872206479742
%e 8 | 8 56 2408 3440024 4221404762120 2337101560809838105414712
%e 9 | 9 72 4104 10599192 44876701584360 327425229254999498091796728
%e 10 | 10 90 6570 28478970 355148098691850 24489214732779742874109277530
%Y Columns and rows: A002378 (k=1), A091940 (k=2), A140986 (k=3), A158348 (k=4), A307334 (n=3).
%Y Cf. A334278, A342088 (analogous for cross-polytope).
%K nonn,tabl
%O 0,4
%A _Peter Kagey_, Feb 28 2021
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