A049391 Expansion of (1-25*x)^(3/5).

1, -15, -75, -875, -13125, -223125, -4090625, -78890625, -1577812500, -32432812500, -681089062500, -14550539062500, -315261679687500, -6911506054687500, -153040491210937500, -3417904303710937500

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• sign
• easy

Examples

			(1-x)^(3/5) = 1 - 3/5*x - 3/25*x^2 - 7/125*x^3 - ...
		

Crossrefs

Cf. A049380.

Programs

Mathematica

CoefficientList[Series[(1-25*x)^(3/5), {x, 0, 15}], x] (* Georg Fischer, Jan 16 2020 *)

Formula

G.f.: (1-25*x)^(3/5).

a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k-3).

a(n) ~ -3/5*Gamma(2/5)^-1*n^(-8/5)*5^(2*n)*{1 + 12/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

Extensions

Definition corrected by Georg Fischer, Jan 16 2020