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%I #18 Jan 21 2024 10:20:00
%S 0,0,0,0,2258870796288,9047768830231276800,506336252436007271792640,
%T 2604852575650929700554897600,2901541315803996724909094338560,
%U 1113635084163037955678982524179968,194993996964612517111634963280691200,18697739035489738337034253081138308480
%N Number of n-edge-colorings of the second Celmins-Swart Snark.
%C The second Celmins-Swart Snark is a cubic graph on 26 vertices and 39 edges with edge chromatic number 4.
%H Alois P. Heinz, <a href="/A159447/b159447.txt">Table of n, a(n) for n = 0..1000</a>
%H Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: <a href="http://dx.doi.org/10.1088/1367-2630/11/2/023001">10.1088/1367-2630/11/2/023001</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Celmins-SwartSnarks.html">Celmins-Swart Snarks</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeColoring.html">Edge Coloring</a>.
%H <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (40, -780, 9880, -91390, 658008, -3838380, 18643560, -76904685, 273438880, -847660528, 2311801440, -5586853480, 12033222880, -23206929840, 40225345056, -62852101650, 88732378800, -113380261800, 131282408400, -137846528820, 131282408400, -113380261800, 88732378800, -62852101650, 40225345056, -23206929840, 12033222880, -5586853480, 2311801440, -847660528, 273438880, -76904685, 18643560, -3838380, 658008, -91390, 9880, -780, 40, -1).
%F a(n) = n^39 -78*n^38 + ... (see Maple program).
%p a:= n-> n^39 -78*n^38 +2977*n^37 -74100*n^36 +1352640*n^35 -19306594*n^34 +224342277*n^33 -2181791404*n^32 +18118893123*n^31 -130452836327*n^30 +823952578392*n^29 -4608389780429*n^28 +22997509515589*n^27 -103033396258400*n^26 +416525331736816*n^25 -1525737772270530*n^24 +5081295004914867*n^23 -15428507680657788*n^22 +42803369770538734*n^21 -108682235921838363*n^20 +252855988591085175*n^19 -539410912179380029*n^18 +1055315901598357898*n^17 -1892867854923086364*n^16 +3109878686211564875*n^15 -4672808797433106398*n^14 +6406393723078014052*n^13 -7987839935998545020*n^12 +9017573199563822008*n^11 -9162177613893661616*n^10 +8311775652268340640*n^9 -6661120231484154048*n^8 +4648572768670421376*n^7 -2769843755431745280*n^6 +1370525684357079552*n^5 -540501319873105920*n^4 +159143872899272704*n^3 -31049988392951808*n^2 +3004158272716800*n: seq(a(n), n=0..12);
%Y Cf. A159304.
%K nonn,easy
%O 0,5
%A _Alois P. Heinz_, Apr 11 2009
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