A049390 Expansion of (1-25*x)^(4/5).

1, -20, -50, -500, -6875, -110000, -1925000, -35750000, -692656250, -13853125000, -283989062500, -5937953125000, -126181503906250, -2717755468750000, -59208244140625000, -1302581371093750000

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• sign
• easy

Examples

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

Crossrefs

Cf. A034688.

Programs

Mathematica

CoefficientList[Series[(1-25x)^(4/5),{x,0,20}],x] (* Harvey P. Dale, Dec 14 2017 *)

Formula

G.f.: (1-25*x)^(4/5).

a(n) = 5^n/n! * product[ k=0..n-1 ] (5*k-4).

a(n) ~ -4/5*Gamma(1/5)^-1*n^(-9/5)*5^(2*n)*{1 + 18/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

Extensions

Definition adjusted by Harvey P. Dale, Dec 14 2017.