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A002882 Nearest integer to Bernoulli number B_{2n}.
(Formerly M4435 N1875)
11
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; refs; listen; history; text; internal format)
OFFSET
0,9
REFERENCES
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).
LINKS
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].
FORMULA
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.
MATHEMATICA
Round[BernoulliB[2*Range[0, 30]]] (* Harvey P. Dale, Sep 14 2012 *)
PROG
(PARI) a(n)=if(n<0, 0, round(bernfrac(2*n))) /* Michael Somos, Apr 15 2005 */
CROSSREFS
Sequence in context: A005012 A123784 A091695 * A094905 A178922 A306046
KEYWORD
sign,easy,nice
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Jan 10 2003
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)