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A002882
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Nearest integer to Bernoulli number B_{2n}.
(Formerly M4435 N1875)
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11
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1, 0, 0, 0, 0, 0, 0, 1, -7, 55, -529, 6192, -86580, 1425517, -27298231, 601580874, -15116315767, 429614643061, -13711655205088, 488332318973593, -19296579341940068, 841693047573682615, -40338071854059455413, 2115074863808199160560, -120866265222965259346027, 7500866746076964366855720
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OFFSET
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0,9
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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, 1964 (and various reprintings), p. 810.
H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 236.
S. Ramanujan, Some Properties of Bernoulli's Numbers, Collected Papers of Srinivasa Ramanujan, p. 8, Ed. G. H. Hardy et al., AMS Chelsea 2000.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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, 1972 [alternative scanned copy].
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FORMULA
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Asymptotic expansion of 1/(2x^2) + Sum_{k>0} 1/(x + k)^2 - 1/(6(x^3 - x)) + Sum_{p>3 prime} 1/(p(x^p - x)) = Sum_{k>=0} a(k)/x^(2k + 1). From Ramanujan.
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<0, 0, round(bernfrac(2*n))) /* Michael Somos, Apr 15 2005 */
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CROSSREFS
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KEYWORD
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sign,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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