A049392 Expansion of (1-25*x)^(2/5).

1, -10, -75, -1000, -16250, -292500, -5606250, -112125000, -2312578125, -48821093750, -1049653515625, -22901531250000, -505742148437500, -11281940234375000, -253843655273437500, -5753789519531250000

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• sign
• easy

Examples

			(1-x)^(2/5) = 1 - 2/5*x - 3/25*x^2 - 8/125*x^3 - ...
		

Links

• Iain Fox, Table of n, a(n) for n = 0..718

Crossrefs

Cf. A049381.

Programs

PARI

first(n) = x='x+O('x^n); Vec((1-25*x)^(2/5)) \\ Iain Fox, Aug 10 2018

Formula

G.f.: (1-25*x)^(2/5).

a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k-2).

a(n) ~ -2/5*Gamma(3/5)^-1*n^(-7/5)*5^(2*n)*{1 + 7/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

Extensions

Definition corrected by Georg Fischer, Jan 16 2020