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%I #29 Jan 20 2024 14:25:37
%S 0,0,0,7200,168506880,112603286160,15108392957760,775405390866960,
%T 20886647215714560,353998543659193440,4231366997071432320,
%U 38508081275604409920,281586666065022616320,1720887594454493527920,9053942417801770507200,41955877772610102690480
%N Number of n-colorings of the dodecahedral graph.
%D N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See pp. 69-70.
%H Eric M. Schmidt, <a href="/A218513/b218513.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/DodecahedralGraph.html">Dodecahedral Graph</a>
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
%F a(n) = n(n-1)(n-2)(n^17 - 27n^16 + 352n^15 - 2950n^14 + 17839n^13 - 82777n^12 + 305866n^11 - 921448n^10 + 2297495n^9 - 4783425n^8 + 8347700n^7 - 12195590n^6 + 14808795n^5 - 14713381n^4 + 11613602n^3 - 6892084n^2 + 2751604n - 555984).
%F See A296919 for the coefficients of the expanded form of a(n). - _N. J. A. Sloane_, Dec 23 2017
%F G.f.: -240*x^3*(2007273*x^17 +678113783*x^16 +62897280675*x^15 +2149103163405*x^14 +32571452423195*x^13 +246267894384141*x^12 +1000326687571911*x^11 +2283861589692665*x^10 +3002531231655465*x^9 +2288662487004975*x^8 +1001857651156729*x^7 +244960098705399*x^6 +31779760521705*x^5 +2006465657455*x^4 +53246253405*x^3 +454442307*x^2 +701482*x +30)/(x-1)^21. - _Colin Barker_, Nov 06 2012
%o (Sage)
%o def A218513(n) : return n*(n-1)*(n-2)*(n^17 -27*n^16 +352*n^15 -2950*n^14 +17839*n^13 -82777*n^12 +305866*n^11 -921448*n^10 +2297495*n^9 -4783425*n^8 +8347700*n^7 -12195590*n^6 +14808795*n^5 -14713381*n^4 +11613602*n^3 -6892084*n^2 +2751604*n -555984);
%o (Maxima)
%o A218513(n):=n*(n-1)*(n-2)*(n^17 -27*n^16 +352*n^15 -2950*n^14 +17839*n^13 -82777*n^12 +305866*n^11 -921448*n^10 +2297495*n^9 -4783425*n^8 +8347700*n^7 -12195590*n^6 +14808795*n^5 -14713381*n^4 +11613602*n^3 -6892084*n^2 +2751604*n -555984)$
%o makelist(A218513(n), n, 0, 30); /* _Martin Ettl_, Nov 03 2012 */
%Y Cf. A052762, A140986, A115400, A218514, A296918, A296919.
%K nonn,easy
%O 0,4
%A _Eric M. Schmidt_, Oct 31 2012
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