Sequence A014509 Misnamed

[Franklin T. Adams-Watters]

Sequence A014509 is not the floor of the Bernoulli numbers B_2n, as it claims, but the truncation.  That is, the values are rounded towards zero, not towards minus infinity.

Also, the sequence shows an exponential generating function, which the E.G.F. for the Bernoulli numbers themselves, not the truncated values.

Corrected entry:

%I A014509
%S A014509 1,0,0,0,0,0,0,1,7,54,529,6192,86580,1425517,27298231,601580873,
%T A014509 15116315767,429614643061,13711655205088,488332318973593,
%U A014509 19296579341940068,841693047573682615,40338071854059455413
%V A014509 1,0,0,0,0,0,0,1,-7,54,-529,6192,-86580,1425517,-27298231,601580873,
%W A014509 -15116315767,429614643061,-13711655205088,488332318973593,
%X A014509 -19296579341940068,841693047573682615,-40338071854059455413
%N A014509 Truncation of Bernoulli number: [|B_2n|] * sign(B_2n).
%D A014509 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Appli\
  ed Math. Series 55, 1964 (and various reprintings), p. 810.
%H A014509 <a href="http://www.research.att.com/~njas/sequences/Sindx_Be.html#Bernoulli">Index entries for sequences re\
  lated to Bernoulli numbers.</a>
%F A014509 abs(a(n)) = 2*(2*n)!/(2*Pi)^(2*n)*(1-sum(k=2,m,1/k^(2n))+O(1/m^(2n))) - Benoit Cloitre (abmt(AT)wanadoo.fr),\
   Jan 29 2003
%Y A014509 Adjacent sequences: A014506 A014507 A014508 this_sequence A014510 A014511 A014512
%Y A014509 Sequence in context: A081008 A015562 A093742 this_sequence A084065 A056719 A043077
%K A014509 sign
%O A014509 0,9
%A A014509 Simon Plouffe (plouffe(AT)math.uqam.ca)


-- 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645


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