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A007509
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Numerator of Sum_{k=0..n} (-1)^k/(2*k+1).
(Formerly M2061)
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10
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1, 2, 13, 76, 263, 2578, 36979, 33976, 622637, 11064338, 11757173, 255865444, 1346255081, 3852854518, 116752370597, 3473755390832, 3610501179557, 3481569435902, 133330680156299, 129049485078524, 5457995496252709
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Denominators of convergents to 4/pi.
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REFERENCES
| P. Beckmann, A History of Pi. Golem Press, Boulder, CO, 2nd ed., 1971, p. 131.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Pi.
Eric Weisstein's World of Mathematics, Pi - Continued Fraction
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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EXAMPLE
| [ 1 ], 2/3, 13/15, 76/105, 263/315, 2578/3465, 36979/45045, 33976/45045, 622637/765765,...
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MAPLE
| A007509 := n->numer(add((-1)^k/(2*k+1), k=0..n));
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MATHEMATICA
| Table[Numerator[FunctionExpand[(Pi + (-1)^n(HarmonicNumber[n/2 + 1/4] - HarmonicNumber[n/2 - 1/4]))/4]], {n, 0, 20}] (* From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Jan 18 2011 *)
Numerator[Table[Sum[(-1)^k/(2k+1), {k, 0, n}], {n, 0, 30}]] (* From Harvey P. Dale, Oct 22 2011 *)
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CROSSREFS
| Denominators are A025547.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 2009: (Start)
Cf. A157142 and A166107.
Appears in A167576, A167577, A167578, A024199, A167588 and A167589.
(End)
Sequence in context: A154357 A161130 A192700 * A077413 A024199 A037523
Adjacent sequences: A007506 A007507 A007508 * A007510 A007511 A007512
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KEYWORD
| nonn,easy,nice,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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