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Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
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%I #8 Jun 13 2015 00:53:55

%S 0,1,1,3,8,21,49,105,210,399,729,1293,2242,3821,6427,10703,17690,

%T 29073,47579,77621,126340,205291,333171,540233,875428,1417961,2295989,

%U 3716875,6016140,9736669,15756869,25498033,41259862,66763351,108029197

%N Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

%C 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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,6,1,-3,1)

%F 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 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 (See A193044.)

%Y Cf. A192232, A192744, A192951, A193044.

%K nonn

%O 0,4

%A _Clark Kimberling_, Jul 15 2011