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A002882 Nearest integer to Bernoulli number B_{2n}.
(Formerly M4435 N1875)
10
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

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.

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 A112243

Adjacent sequences:  A002879 A002880 A002881 * A002883 A002884 A002885

KEYWORD

sign,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Jan 10 2003

STATUS

approved

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Last modified January 24 04:31 EST 2018. Contains 298115 sequences.