A002882 Nearest integer to Bernoulli number B_{2n}.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy
• nice

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

• 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.

Programs

Mathematica

Round[BernoulliB[2*Range[0,30]]] (* Harvey P. Dale, Sep 14 2012 *)

PARI

a(n)=if(n<0,0,round(bernfrac(2*n))) /* Michael Somos, Apr 15 2005 */

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.

Extensions

More terms from Vladeta Jovovic, Jan 10 2003