A193044 -id:A193044 - cp's OEIS frontend

A193045 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 1, 3, 8, 21, 49, 105, 210, 399, 729, 1293, 2242, 3821, 6427, 10703, 17690, 29073, 47579, 77621, 126340, 205291, 333171, 540233, 875428, 1417961, 2295989, 3716875, 6016140, 9736669, 15756869, 25498033, 41259862, 66763351, 108029197

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Clark Kimberling, Jul 15 2011

nonn

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.

Index entries for linear recurrences with constant coefficients, signature (5,-9,6,1,-3,1)

Cf. A192232, A192744, A192951, A193044.

Mathematica
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(See A193044.)
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a(n)=5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).

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

cp's OEIS Frontend

A193045 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

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