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Search: id:A127676
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| A127676 |
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Numerators of partial sums of a series for Pi*sqrt(2)/4. |
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+0
2
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| 1, 4, 17, 104, 347, 4132, 50251, 47248, 848261, 16882724, 16189889, 357817912, 1856017421, 5753962988, 161845337077, 4871637351712, 5008383140437, 5137314884092, 185568039683479, 181286844605704, 7599727236867089
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OFFSET
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0,2
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COMMENT
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Denominators coincide with A025547(n+1) for n=0..41, but then start to differ. See the W. Lang link. denominator(r(42))=7422822568422519986207785205976075 but the corresponding entry is A025547(43)=126187983663182839765532348501593275.
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REFERENCES
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R. Ayoub, Euler and the Zeta Function, Am. Math. Monthly 81 (1974) 1067-1086, p. 1077.
E. Maor, Trigonometric Delights, Princeton University Press, 1998, p. 205.
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LINKS
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W. Lang, Rationals and limit.
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FORMULA
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a(n)=numerator(r(n)) with the rationals (in lowest terms) r(n):=sum((-1)^floor(k/2)/(2*k+1),k=0..n).
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EXAMPLE
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Rationals r(n): [1, 4/3, 17/15, 104/105, 347/315, 4132/3465,...].
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CROSSREFS
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Sequence in context: A024052 A128321 A091635 this_sequence A122940 A077386 A004140
Adjacent sequences: A127673 A127674 A127675 this_sequence A127677 A127678 A127679
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Mar 07 2007
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