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A193047
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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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1
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0, 1, 2, 19, 102, 377, 1104, 2777, 6282, 13155, 25998, 49153, 89792, 159681, 278034, 476131, 804790, 1346457, 2234768, 3686201, 6051290, 9897491, 16143262, 26275009, 42698112, 69304897, 112393634, 182155507, 295080582, 477850745
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OFFSET
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0,3
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COMMENTS
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The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+n^4, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.
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LINKS
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FORMULA
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a(n)=6*a(n-1)-14*a(n-2)+15*a(n-3)-5*a(n-4)-4*a(n-5)+4*a(n-6)-a(n-7).
G.f.: -x*(-1+4*x-21*x^2-x^3-6*x^4+x^5) / ( (x^2+x-1)*(x-1)^5 ). - R. J. Mathar, May 12 2014
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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