A049381 Expansion of (1-25*x)^(-3/5).

1, 15, 300, 6500, 146250, 3363750, 78487500, 1850062500, 43938984375, 1049653515625, 25191684375000, 606890578125000, 14666522304687500, 355381117382812500, 8630684279296875000, 210013317462890625000

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..715

Formula

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

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

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

a(n) = (-25)^n*binomial(-3/5, n). - Peter Luschny, Oct 23 2018

From Peter Bala, Sep 24 2023: (Start)

a(n) = 25^n * binomial(n - 2/5, n).

P-recursive: a(n) = 5*(5*n - 2)/n * a(n-1) with a(0) = 1. (End)

Example

(1-x)^(-3/5) = 1 + 3/5*x + 12/25*x^2 + 52/125*x^3 + ...

Maple

A049381 := n -> (-25)^n*binomial(-3/5, n):
seq(A049381(n), n=0..16); # Peter Luschny, Oct 23 2018

Mathematica

CoefficientList[Series[(1-25x)^(-3/5), {x, 0, 20}], x] (* Harvey P. Dale, Aug 08 2013 *)

Crossrefs

Cf. A034688, A049380, A049382, A049392, A049396.

Sequence in context: A144349 A375222 A009064 * A051691 A247238 A353145

Adjacent sequences: A049378 A049379 A049380 * A049382 A049383 A049384

Keyword

nonn,easy

Author

Joe Keane (jgk(AT)jgk.org)

Status

approved