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Search: id:A060054
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| A060054 |
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Numerators of numbers appearing in the Euler-Maclaurin summation formula. |
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+0
4
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| -1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -691, 0, 1, 0, -3617, 0, 43867, 0, -174611, 0, 77683, 0, -236364091, 0, 657931, 0, -3392780147, 0, 1723168255201, 0, -7709321041217, 0, 151628697551, 0, -26315271553053477373
(list; graph; listen)
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OFFSET
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1,12
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COMMENT
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a(n+1)=numerator(-Zeta(-n)), n>=1, with Riemann's zeta function. a(1)=-1=-numerator(-Zeta(-0)). For denominators see A075180.
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, December 1972, p. 16 (3.6.28), p. 806 (23.1.30), p. 886 (25.4.7).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, December 1972, p. 16 (3.6.28), p. 806 (23.1.30), p. 886 (25.4.7).
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FORMULA
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a(n)= numerator(b(n)) with b(1) = -1/2; b(2*k+1) = 0, k >= 1; b(2*k) = B(2*k)/(2*k)! (B(2*n) = B_2n Bernoulli numbers: numerators A000367, denominators A002445)
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CROSSREFS
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Denominators of nonzero numbers give A060055.
Cf. A001067 (numerator of B(2*k)/(2*k)).
Sequence in context: A025347 A078877 A115177 this_sequence A120082 A120084 A046968
Adjacent sequences: A060051 A060052 A060053 this_sequence A060055 A060056 A060057
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KEYWORD
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sign,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 16 2001
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