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A363571
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Expansion of (1 / sqrt(1 - 10*x + 9*x^2) - 1 / (1 - x)) / 4.
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1
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0, 1, 8, 61, 480, 3881, 31976, 266981, 2251136, 19124881, 163452168, 1403748941, 12104113632, 104723793721, 908680775528, 7904234296181, 68905275700736, 601832985410081, 5265459181363976, 46137526574521181, 404821208100919520, 3556361565584509001
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp(x) * (exp(4*x) * BesselI(0,4*x) - 1) / 4.
a(n) = Sum_{k=1..n} binomial(n,k)^2 * 4^(k-1).
a(n) = (3^n * LegendreP(n,5/3) - 1) / 4.
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MATHEMATICA
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nmax = 21; CoefficientList[Series[(1/Sqrt[1 - 10 x + 9 x^2] - 1/(1 - x))/4, {x, 0, nmax}], x]
nmax = 21; CoefficientList[Series[Exp[x] (Exp[4 x] BesselI[0, 4 x] - 1)/4, {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k]^2 4^(k - 1), {k, 1, n}], {n, 0, 21}]
Table[(3^n LegendreP[n, 5/3] - 1)/4, {n, 0, 21}]
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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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