A049382 Expansion of (1-25*x)^(-4/5).
1, 20, 450, 10500, 249375, 5985000, 144637500, 3512625000, 85620234375, 2092939062500, 51277007031250, 1258617445312500, 30941012197265625, 761624915625000000, 18768613992187500000, 462959145140625000000
Offset: 0
Examples
(1-x)^(-4/5) = 1 + 4/5*x + 18/25*x^2 + 84/125*x^3 + ...
Programs
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Maple
A049382 := n -> (-25)^n*binomial(-4/5, n): seq(A049382(n), n=0..16); # Peter Luschny, Oct 23 2018
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Mathematica
CoefficientList[Series[(1-25x)^(-4/5),{x,0,20}],x] (* Harvey P. Dale, Oct 24 2021 *) -
PARI
a(n) = prod(k=1, n, 25 - 5/k); \\ Michel Marcus, Jun 13 2018
Formula
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) = Product_{k=1..n} (25 - 5/k). - Michel Lagneau, Sep 16 2012
a(n) = (-25)^n*binomial(-4/5, n). - Peter Luschny, Oct 23 2018
From Peter Bala, Sep 24 2023: (Start)
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)