Search: id:A002882
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%I A002882 M4435 N1875
%S A002882 1,0,0,0,0,0,0,1,7,55,529,6192,86580,1425517,27298231,601580874,15116315767,
%T A002882 429614643061,13711655205088,488332318973593,19296579341940068,841693047573682615,
%U A002882 40338071854059455413,2115074863808199160560,120866265222965259346027,
               7500866746076964366855720
%V A002882 1,0,0,0,0,0,0,1,-7,55,-529,6192,-86580,1425517,-27298231,601580874,-15116315767,
%W A002882 429614643061,-13711655205088,488332318973593,-19296579341940068,841693047573682615,
%X A002882 -40338071854059455413,2115074863808199160560,-120866265222965259346027,
               7500866746076964366855720
%N A002882 Nearest integer to Bernoulli number B_{2n}.
%D A002882 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002882 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002882 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 A002882 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 A002882 S. Ramanujan, Some Properties of Bernoulli's Numbers, Collected Papers 
               of Srinivasa Ramanujan, p. 8, Ed. G. H. Hardy et al., AMS Chelsea 
               2000.
%H A002882 N. J. A. Sloane, <a href="b002882.txt">Table of n, a(n) for n = 0..200</
               a>
%H A002882 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A002882 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%F A002882 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.
%o A002882 (PARI) a(n)=if(n<0,0,round(bernfrac(2*n))) /* Michael Somos Apr 15 2005 
               */
%Y A002882 Sequence in context: A005012 A123784 A091695 this_sequence A094905 A112243 
               A083836
%Y A002882 Adjacent sequences: A002879 A002880 A002881 this_sequence A002883 A002884 
               A002885
%K A002882 sign,easy,nice
%O A002882 0,9
%A A002882 N. J. A. Sloane (njas(AT)research.att.com).
%E A002882 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 10 2003

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