A157327 Egyptian fraction expansion for Pi/4 = arctan(1/2) + arctan(1/3) (Hutton 1776).

2, 3, -24, -81, 160, 1215, -896, -15309, 4608, 177147, -22528, -1948617, 106496, 20726199, -491520, -215233605, 2228224, 2195382771, -9961472, -22082967873, 44040192, 219667417263, -192937984, -2165293113021, 838860800

Offset: 0

Author

Jaume Oliver Lafont, Feb 27 2009

Keywords

• frac
• sign

Comments

Sum_{n>=0} 1/a(n) = Pi/4.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• X. Gourdon and P. Sebah, The constant Pi. The classic period

Crossrefs

Cf. A157142, A155988, A058962.

Programs

Mathematica

CoefficientList[Series[2 (1 - 4 x^2)/(1 + 4 x^2)^2 + 3 x (1 - 9 x^2)/(1 + 9 x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)

Formula

G.f.: 2*(1-4*x^2)/(1+4*x^2)^2 + 3*x*(1-9*x^2)/(1+9*x^2)^2.