0,1

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).

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

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

Cf. A019683, A072172, A072173.

Sequence in context: A094630 A015940 A093853 this_sequence A024072 A119549 A004805

Adjacent sequences: A157329 A157330 A157331 this_sequence A157333 A157334 A157335

frac,sign

Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 27 2009