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A135645 Polynomial expansion of p(x)=(-17 - 98 x^9 + x^10)(-1 - 2 x^9 + x^10)^3(-1 - x^9 + x^10)^6 as: 1/(p(1/x)*x^100). 0

%I

%S 1,110,10861,1064784,104350518,10226356908,1002182997326,

%T 98213933800552,9624965512636055,943246620238838634,

%U 92438168783407537949,9058940540773942228850,887776172995846347486624

%N Polynomial expansion of p(x)=(-17 - 98 x^9 + x^10)(-1 - 2 x^9 + x^10)^3(-1 - x^9 + x^10)^6 as: 1/(p(1/x)*x^100).

%C Matrix polynomial of three level 10by10 10 person game as 100by100 Matrix Markov.

%F p(x)=(-17 - 98 x^9 + x^10)(-1 - 2 x^9 + x^10)^3(-1\) - x^9 + x^10)^6 a(n) = expansion of(1/(p(1/x)*x^100))

%t f[x_] = Product[CharacteristicPolynomial[{{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, a}}, x]^(6/a), {a, 1, 2}]*CharacteristicPolynomial[{{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {17, 0, 0, 0, 0, 0, 0, 0, 0, 98}}, x]; g[x_] = Expand[x^100*f[1/x]]; a = Table[ SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]

%K nonn,uned

%O 1,2

%A _Roger L. Bagula_, Jan 31 2008

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)