id:A157142 - OEIS Search Results

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Denominators of Leibniz series for Pi/4

+0
7

1, -3, 5, -7, 9, -11, 13, -15, 17, -19, 21, -23, 25, -27, 29, -31, 33, -35, 37, -39, 41, -43, 45, -47, 49, -51, 53, -55, 57, -59, 61, -63, 65, -67, 69, -71, 73, -75, 77, -79, 81, -83, 85, -87, 89, -91, 93, -95, 97, -99, 101, -103, 105, -107, 109, -111, 113, -115 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`Numerators are all 1.` `Sum_{n=0..inf}1/a(n)=Pi/4`
	LINKS	`X. Gourdon and P. Sebah, Archimedes' constant` `Mathpages, How Leibniz might have anticipated Euler` `Wikipedia, Leibniz formula for Pi`
	FORMULA	`G.f.:(1-x)/(1+x)^2` `a(0)=1, a(1)=-3, a(n)=-2a(n-1)-a(n-2) for n>=2`
	PROGRAM	`(PARI) a(n)=(2n+1)(-1)^n`
	CROSSREFS	`a(n)=A005408(n)*A033999(n).` `Cf. A157327. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 03 2009]` `Sequence in context: A081874 A165747 A053229 this_sequence A004273 A005408 A144396` `Adjacent sequences: A157139 A157140 A157141 this_sequence A157143 A157144 A157145`
	KEYWORD	`frac,sign`
	AUTHOR	`Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 24 2009`

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Last modified December 8 08:31 EST 2009. Contains 170430 sequences.

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