A049395 Expansion of (1-25*x)^(-7/5).

1, 35, 1050, 29750, 818125, 22089375, 589050000, 15567750000, 408653437500, 10670395312500, 277430278125000, 7187966296875000, 185689129335937500, 4785066025195312500, 123044554933593750000, 3158143576628906250000

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..713

Crossrefs

Cf. A049380.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 16); Coefficients(R!( (1-25*x)^(-7/5) )); // Marius A. Burtea, Jan 16 2020

Maple

f:= gfun:-rectoproc({a(n) = (25+10/n)*a(n-1), a(0) = 1}, a(n), remember):
map(f, [$1..50]); # Robert Israel, Mar 15 2020

Mathematica

CoefficientList[Series[(1-25*x)^(-7/5), {x, 0, 15}], x] (* Georg Fischer, Jan 16 2020 *)

Formula

G.f.: (1-25*x)^(-7/5).

a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k+7).

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

a(n) = (25+10/n)*a(n-1) for n >= 1. - Robert Israel, Mar 15 2020

Extensions

Typo in name corrected by Georg Fischer, Jan 16 2020