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A193049
Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
1
0, 1, 1, 2, 4, 12, 37, 105, 268, 625, 1355, 2772, 5414, 10188, 18605, 33161, 57954, 99683, 169265, 284452, 474066, 784852, 1292567, 2119923, 3465620, 5651323, 9197673, 14947276, 24263704, 39353486, 63787101, 103341963, 167366400, 270986619
OFFSET
0,4
COMMENTS
The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+n(4-5*n^2+n^4)/120, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.
FORMULA
a(n)=7*a(n-1)-20*a(n-2)+29*a(n-3)-20*a(n-4)+*a(n-5)+8*a(n-6)-5*a(n-7)+a(n-8).
G.f.: -x*(x^2-x+1)*(x^4-5*x^3+9*x^2-5*x+1) / ( (x^2+x-1)*(x-1)^6 ). - R. J. Mathar, May 12 2014
MATHEMATICA
(See A193048.)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 15 2011
STATUS
approved