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A049382 Expansion of (1-25*x)^(-4/5). 14
1, 20, 450, 10500, 249375, 5985000, 144637500, 3512625000, 85620234375, 2092939062500, 51277007031250, 1258617445312500, 30941012197265625, 761624915625000000, 18768613992187500000, 462959145140625000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

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

EXAMPLE

(1-x)^(-4/5) = 1 + 4/5*x + 18/25*x^2 + 84/125*x^3 + ...

MAPLE

A049382 := n -> (-25)^n*binomial(-4/5, n):

seq(A049382(n), n=0..16); # Peter Luschny, Oct 23 2018

PROG

(PARI) a(n) = prod(k=1, n, 25 - 5/k); \\ Michel Marcus, Jun 13 2018

CROSSREFS

Cf. A008546, A049393, A049397, A049381.

Sequence in context: A099278 A276452 A111158 * A288034 A272553 A268884

Adjacent sequences:  A049379 A049380 A049381 * A049383 A049384 A049385

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified May 28 10:49 EDT 2020. Contains 334681 sequences. (Running on oeis4.)