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A157332 Denominators of Egyptian fraction for Pi/16 based on Machin's formula 3
5, -956, -375, 163823028, 15625, -15596225303980, -546875, 1247220779824098212, 17578125, -91597497639855832244124, -537109375, 6394838587727583881086964116, 15869140625, -431694043145875922302762745864588, -457763671875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Machin's formula: Pi/4 = 4atan(1/5) - atan(1/239). Sum_{n>=0} 1/a(n) = Pi/16 = atan(1/5) - (1/4)atan(1/239).

LINKS

Table of n, a(n) for n=0..14.

X. Gourdon and P. Sebah, Collection of series for Pi

FORMULA

a(2n)=(2n+1)*5^(2n+1)*(-1)^n, a(2n+1)=-4*(2n+1)239^(2n+1)*(-1)^n

G.f.: 5*(1-25*x^2)/(1+25*x^2)^2-956*x*(1-57121*x^2)/(1+57121*x^2)^2

CROSSREFS

Cf. A019683, A072172, A072173.

Sequence in context: A195627 A318066 A216375 * A229203 A024072 A119549

Adjacent sequences:  A157329 A157330 A157331 * A157333 A157334 A157335

KEYWORD

frac,sign,easy

AUTHOR

Jaume Oliver Lafont, Feb 27 2009

EXTENSIONS

More terms from Colin Barker, Aug 07 2013

STATUS

approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)