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%I #12 Aug 13 2013 20:20:39
%S 1,3906,3000366,414425080,19064362455,428429377026,5861180425996,
%T 55823546748096,403783634784285,2353615149832210,11531349080992026,
%U 48981767072238936,184656623163700051,629125059062885490,1964980839044519640,5691311662142685376
%N 1/2 the number of colorings of a 4 X 4 square array with n colors.
%H Alois P. Heinz, <a href="/A068240/b068240.txt">Table of n, a(n) for n = 2..1000</a>
%F From _Alois P. Heinz_, Apr 27 2012 (Start)
%F G.f.: -(2507986*x^14 +349887529*x^13 +12282125725*x^12 +158263444274*x^11 +896159384816*x^10 +2455337616143*x^9 +3417678462327*x^8 +2453922059100*x^7 +895941969162*x^6 +158666067383*x^5 +12424532171*x^4 +363949394*x^3 +2934100*x^2 +3889*x+1)*x^2 / (x-1)^17.
%F a(n) = n*(n-1)*(n^14 -23*n^13 +253*n^12 -1762*n^11 +8675*n^10 -31939*n^9 +90723*n^8 -202160*n^7 +355622*n^6 -492434*n^5 +529770*n^4 -430857*n^3 +251492*n^2 -94782*n +17493)/2.
%F (End)
%p a:= n-> n*(n-1)*(17493+(-94782+(251492+(-430857+(529770+(-492434 +(355622+(-202160+(90723+(-31939+(8675+(-1762+(253 +(-23+n)*n)*n) *n)*n)*n)*n) *n)*n) *n)*n) *n)*n)*n) /2:
%p seq(a(n), n=2..30); # _Alois P. Heinz_, Apr 27 2012
%Y Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.
%K nonn
%O 2,2
%A _R. H. Hardin_, Feb 24 2002
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