A049380 Expansion of (1-25*x)^(-2/5).
1, 10, 175, 3500, 74375, 1636250, 36815625, 841500000, 19459687500, 454059375000, 10670395312500, 252209343750000, 5989971914062500, 142837791796875000, 3417904303710937500, 82029703289062500000
Offset: 0
Examples
(1-x)^(-2/5) = 1 + 2/5*x + 7/25*x^2 + 28/125*x^3 + ...
Links
- Robert Israel, Table of n, a(n) for n = 0..716
Programs
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Maple
f:= gfun:-rectoproc({a(n+1) = (10+25*n)*a(n)/(n+1),a(0)=1},a(n),remember): map(f, [$0..50]); # Robert Israel, Sep 04 2018 -
Mathematica
CoefficientList[Series[1/Surd[(1-25x)^2,5],{x,0,20}],x] (* Harvey P. Dale, Jan 15 2024 *) -
PARI
x='x+O('x^99); Vec((1-25*x)^(-2/5)) \\ Altug Alkan, Sep 04 2018
Formula
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+1) = (10 + 25*n)*a(n)/(n+1). - Robert Israel, Sep 04 2018
a(n) = (-25)^n*binomial(-2/5,n). - Peter Luschny, Oct 23 2018
From Peter Bala, Sep 24 2023: (Start)
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)