A049381 Expansion of (1-25*x)^(-3/5).
1, 15, 300, 6500, 146250, 3363750, 78487500, 1850062500, 43938984375, 1049653515625, 25191684375000, 606890578125000, 14666522304687500, 355381117382812500, 8630684279296875000, 210013317462890625000
Offset: 0
Examples
(1-x)^(-3/5) = 1 + 3/5*x + 12/25*x^2 + 52/125*x^3 + ...
Links
- Robert Israel, Table of n, a(n) for n = 0..715
Programs
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Maple
A049381 := n -> (-25)^n*binomial(-3/5, n): seq(A049381(n), n=0..16); # Peter Luschny, Oct 23 2018
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Mathematica
CoefficientList[Series[(1-25x)^(-3/5),{x,0,20}],x] (* Harvey P. Dale, Aug 08 2013 *)
Formula
G.f.: (1-25*x)^(-3/5).
a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k+3).
a(n) ~ Gamma(3/5)^-1*n^(-2/5)*5^(2*n)*{1 - 3/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = (-25)^n*binomial(-3/5, n). - Peter Luschny, Oct 23 2018
From Peter Bala, Sep 24 2023: (Start)
a(n) = 25^n * binomial(n - 2/5, n).
P-recursive: a(n) = 5*(5*n - 2)/n * a(n-1) with a(0) = 1. (End)