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%I #25 Sep 24 2023 09:15:39
%S 1,20,450,10500,249375,5985000,144637500,3512625000,85620234375,
%T 2092939062500,51277007031250,1258617445312500,30941012197265625,
%U 761624915625000000,18768613992187500000,462959145140625000000
%N Expansion of (1-25*x)^(-4/5).
%F G.f.: (1-25*x)^(-4/5).
%F a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k + 4).
%F 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
%F a(n) = Product_{k=1..n} (25 - 5/k). - _Michel Lagneau_, Sep 16 2012
%F a(n) = (-25)^n*binomial(-4/5, n). - _Peter Luschny_, Oct 23 2018
%F From _Peter Bala_, Sep 24 2023: (Start)
%F a(n) = 25^n * binomial(n - 1/5, n).
%F P-recursive: a(n) = 5*(5*n - 1)/n * a(n-1) with a(0) = 1. (End)
%e (1-x)^(-4/5) = 1 + 4/5*x + 18/25*x^2 + 84/125*x^3 + ...
%p A049382 := n -> (-25)^n*binomial(-4/5, n):
%p seq(A049382(n), n=0..16); # _Peter Luschny_, Oct 23 2018
%t CoefficientList[Series[(1-25x)^(-4/5),{x,0,20}],x] (* _Harvey P. Dale_, Oct 24 2021 *)
%o (PARI) a(n) = prod(k=1, n, 25 - 5/k); \\ _Michel Marcus_, Jun 13 2018
%Y Cf. A008546, A034688, A049393, A049397, A049381, A049382.
%K nonn,easy
%O 0,2
%A Joe Keane (jgk(AT)jgk.org)
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