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A380589 Number of n-colorings of the Hypercube Graph Q5.

%I A380589 #19 Jul 06 2025 18:57:21
%S A380589 0,0,2,1185282,130253748108,2157531034816940,7905235551766437150,
%T A380589 7365707045872206479742,2337101560809838105414712,
%U A380589 327425229254999498091796728,24489214732779742874109277530,1119349138930999380736025706650,34471067091433681765512048700932
%N A380589 Number of n-colorings of the Hypercube Graph Q5.
%C A380589 The Hypercube Graph Q5 has 32 vertices and 80 edges.
%C A380589 All terms are even.
%H A380589 Alois P. Heinz, <a href="/A380589/b380589.txt">Table of n, a(n) for n = 0..10000</a>
%H A380589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A380589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A380589 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (33, -528, 5456, -40920, 237336, -1107568, 4272048, -13884156, 38567100, -92561040, 193536720, -354817320, 573166440, -818809200, 1037158320, -1166803110, 1166803110, -1037158320, 818809200, -573166440, 354817320, -193536720, 92561040, -38567100, 13884156, -4272048, 1107568, -237336, 40920, -5456, 528, -33, 1).
%F A380589 a(n) = n^32 - 80*n^31 + 3160*n^30 - ... (see Maple program).
%p A380589 a:= n-> (((((((((((((((((((((((((((((((n-80)*n+3160)*n-82080)*n+1575420)*n
%p A380589     -23805776)*n+294640000)*n-3068289720)*n+27406254870)*n-212981036784)*n
%p A380589     +1455643449120)*n-8822129447280)*n+47712047044920)*n-231347639674200)*n
%p A380589     +1009138022379076)*n-3968583456247214)*n+14086095737441185)*n-45124968898112160)*n
%p A380589     +130327084318442384)*n-338572422663483544)*n+788328935798745052)*n
%p A380589     -1636781898149840504)*n+3009654466362869780)*n-4856773984500880124)*n
%p A380589     +6797172300402030636)*n-8122089299204814072)*n+8114599308192145448)*n
%p A380589     -6584797184952049568)*n+4160914137061367054)*n-1915734714629493936)*n
%p A380589     +569711421560808713)*n-81768640551939777)*n:
%p A380589 seq(a(n), n=0..12);
%Y A380589 Column k=5 of A342128.
%Y A380589 Cf. A001477, A002378, A091940, A140986, A158348, A334278.
%K A380589 nonn,easy
%O A380589 0,3
%A A380589 _Alois P. Heinz_, Jan 27 2025