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%I A193045 #8 Jun 13 2015 00:53:55
%S A193045 0,1,1,3,8,21,49,105,210,399,729,1293,2242,3821,6427,10703,17690,
%T A193045 29073,47579,77621,126340,205291,333171,540233,875428,1417961,2295989,
%U A193045 3716875,6016140,9736669,15756869,25498033,41259862,66763351,108029197
%N A193045 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
%C A193045 The titular polynomials are defined recursively:  p(n,x)=x*p(n-1,x)+n(-1+n^2)/6, with p(0,x)=1.  For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.
%H A193045 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,6,1,-3,1)
%F A193045 a(n)=5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).
%F A193045 G.f.: -x*(1-4*x+7*x^2-4*x^3+x^4) / ( (x^2+x-1)*(x-1)^4 ). - _R. J. Mathar_, May 12 2014
%t A193045 (See A193044.)
%Y A193045 Cf. A192232, A192744, A192951, A193044.
%K A193045 nonn
%O A193045 0,4
%A A193045 _Clark Kimberling_, Jul 15 2011

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