%I M4435 N1875 #30 May 08 2018 15:11:53

%S 1,0,0,0,0,0,0,1,-7,55,-529,6192,-86580,1425517,-27298231,601580874,

%T -15116315767,429614643061,-13711655205088,488332318973593,

%U -19296579341940068,841693047573682615,-40338071854059455413,2115074863808199160560,-120866265222965259346027,7500866746076964366855720

%N Nearest integer to Bernoulli number B_{2n}.

%D 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.

%D 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.

%D S. Ramanujan, Some Properties of Bernoulli's Numbers, Collected Papers of Srinivasa Ramanujan, p. 8, Ed. G. H. Hardy et al., AMS Chelsea 2000.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H N. J. A. Sloane, <a href="/A002882/b002882.txt">Table of n, a(n) for n = 0..200</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%F 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.

%t Round[BernoulliB[2*Range[0,30]]] (* _Harvey P. Dale_, Sep 14 2012 *)

%o (PARI) a(n)=if(n<0,0,round(bernfrac(2*n))) /* _Michael Somos_, Apr 15 2005 */

%K sign,easy,nice

%O 0,9

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Jan 10 2003