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A049380
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Expansion of (1-25*x)^(-2/5).
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5
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1, 10, 175, 3500, 74375, 1636250, 36815625, 841500000, 19459687500, 454059375000, 10670395312500, 252209343750000, 5989971914062500, 142837791796875000, 3417904303710937500, 82029703289062500000
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-25*x)^(-2/5).
a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k + 2).
a(n) ~ Gamma(2/5)^(-1)*n^(-3/5)*5^(2*n)*{1 - 3/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = 25^n * binomial(n - 3/5, n).
P-recursive: a(n) = 5*(5*n - 3)/n * a(n-1) with a(0) = 1. (End)
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EXAMPLE
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(1-x)^(-2/5) = 1 + 2/5*x + 7/25*x^2 + 28/125*x^3 + ...
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MAPLE
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f:= gfun:-rectoproc({a(n+1) = (10+25*n)*a(n)/(n+1), a(0)=1}, a(n), remember):
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MATHEMATICA
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CoefficientList[Series[1/Surd[(1-25x)^2, 5], {x, 0, 20}], x] (* Harvey P. Dale, Jan 15 2024 *)
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PROG
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(PARI) x='x+O('x^99); Vec((1-25*x)^(-2/5)) \\ Altug Alkan, Sep 04 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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STATUS
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approved
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