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A049382
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Expansion of (1-25*x)^(-4/5).
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15
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1, 20, 450, 10500, 249375, 5985000, 144637500, 3512625000, 85620234375, 2092939062500, 51277007031250, 1258617445312500, 30941012197265625, 761624915625000000, 18768613992187500000, 462959145140625000000
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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)^(-4/5).
a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k + 4).
a(n) ~ Gamma(4/5)^-1*n^(-1/5)*5^(2*n)*{1 - 2/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = 25^n * binomial(n - 1/5, n).
P-recursive: a(n) = 5*(5*n - 1)/n * a(n-1) with a(0) = 1. (End)
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EXAMPLE
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(1-x)^(-4/5) = 1 + 4/5*x + 18/25*x^2 + 84/125*x^3 + ...
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MAPLE
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A049382 := n -> (-25)^n*binomial(-4/5, n):
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MATHEMATICA
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CoefficientList[Series[(1-25x)^(-4/5), {x, 0, 20}], x] (* Harvey P. Dale, Oct 24 2021 *)
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PROG
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(PARI) a(n) = prod(k=1, n, 25 - 5/k); \\ Michel Marcus, Jun 13 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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