A049397 Expansion of (1-25*x)^(-9/5).

1, 45, 1575, 49875, 1496250, 43391250, 1229418750, 34248093750, 941822578125, 25638503515625, 692239594921875, 18564607318359375, 495056195156250000, 13138029794531250000, 347219358855468750000

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• nonn
• easy

Examples

			(1-25*x)^(-9/5) = 1 + 9/5*(5^2*x) + 63/25*(5^2*x)^2 + 399/125*(5^2*x)^3 + ... = 1 + 5*9*x + 63*5^2* x^2 + 399*5^3*x^3 + ... = 1 + 45*x + 1575*x^2 + 49875*x^3 + ...
		

Links

• Todd Silvestri, Table of n, a(n) for n = 0..713

Crossrefs

Cf. A049382.

Programs

Mathematica

a[n_Integer/;n>=0]:=25^n Pochhammer[9/5,n]/n! (* Todd Silvestri, Dec 17 2014 *)

Formula

G.f.: (1-25*x)^(-9/5).

a(n) = 5^n/n! * product[ k=0..n-1 ] (5*k+9).

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

a(n) = (25^n*(9/5)n)/n!, where the rising factorial (c)_n = Gamma(c+n)/Gamma(c). - _Todd Silvestri, Dec 17 2014. See the a(n) formula above.

Extensions

Edited: name and example corrected according to G.f. - Wolfdieter Lang, Jan 05 2015