A049396 Expansion of (1-25*x)^(-8/5).

1, 40, 1300, 39000, 1121250, 31395000, 863362500, 23434125000, 629792109375, 16794456250000, 445053090625000, 11733217843750000, 307996968398437500, 8055305327343750000, 210013317462890625000, 5460346254035156250000

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• nonn
• easy

Examples

			(1-25*x)^(-8/5) = 1+40*x+1300*x^2+39000*x^3+1121250*x^4+31395000*x^5+...
		

Crossrefs

Cf. A049381.

Programs

Mathematica

CoefficientList[Series[(1-25x)^-(8/5),{x,0,20}],x] (* Harvey P. Dale, May 06 2016 *)

Formula

G.f.: (1-25*x)^(-8/5).

a(n) = (5^n/n!) * product[ k=0..n-1 ] (5*k+8).

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

Extensions

Typo in definition corrected by N. J. A. Sloane, May 06 2016