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A288839 Triangle read by rows: coefficients of the chromatic polynomial of the n-Hanoi graph.

%I A288839 #9 Feb 16 2025 08:33:48
%S A288839 0,2,-3,1,0,40,-180,370,-455,363,-190,63,-12,1,0,608000,-6960000,
%T A288839 40524800,-158999200,468979200,-1099617480,2117585600,-3419826630,
%U A288839 4697231261,-5541107684,5652058863,-5007519752,3863562996,-2598606825,1522861581,-776022242,342624075,-130362394,42424338,-11689056,2689452,-507084,76293,-8806,732,-39,1
%N A288839 Triangle read by rows: coefficients of the chromatic polynomial of the n-Hanoi graph.
%C A288839 Equal to A193233 with ordering of row elements reversed.
%H A288839 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A288839 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a>
%e A288839 Polynomials:
%e A288839 (x-2)*(x-1)*x
%e A288839 (x-2)^3*(x-1)*x*(5-10*x+10*x^2-5*x^3+x^4)
%e A288839 (x-2)^6*(x-1)*x*(-9500+70750*x+...+x^19)
%e A288839 Coefficients:
%e A288839 0, 2, -3, 1;
%e A288839 0, 40, -180, 370, -455, 363, -190, 63, -12, 1;
%e A288839 0, 608000, -6960000, 40524800, -158999200, ..., -39, 1;
%Y A288839 Cf. A193233 (chromatic polynomial with highest coefficients first).
%Y A288839 Cf. A137889 (directed Hamiltonian paths in the n-Hanoi graph).
%Y A288839 Cf. A288490 (independent vertex sets in the n-Hanoi graph).
%Y A288839 Cf. A286017 (matchings in the n-Hanoi graph).
%Y A288839 Cf. A193136 (spanning trees of the n-Hanoi graph).
%Y A288839 Cf. A288796 (undirected paths in the n-Hanoi graph).
%K A288839 sign,tabf
%O A288839 1,2
%A A288839 _Eric W. Weisstein_, Jun 17 2017