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Search: id:A002882
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| A002882 |
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Nearest integer to Bernoulli number B_{2n}.
(Formerly M4435 N1875)
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+0
8
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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
(list; graph; listen)
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OFFSET
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0,9
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..200
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].
Index entries for sequences related to Bernoulli numbers.
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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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PROGRAM
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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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Sequence in context: A005012 A123784 A091695 this_sequence A094905 A112243 A083836
Adjacent sequences: A002879 A002880 A002881 this_sequence A002883 A002884 A002885
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KEYWORD
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sign,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 10 2003
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