Search: id:A002427
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%I A002427 M2510 N0993
%S A002427 1,1,1,1,3,5,691,35,3617,43867,1222277,854513,1181820455,76977927,
%T A002427 23749461029,8615841276005,84802531453387,90219075042845,26315271553053477373,
%U A002427 38089920879940267,261082718496449122051,1520097643918070802691
%V A002427 1,1,-1,1,-3,5,-691,35,-3617,43867,-1222277,854513,-1181820455,76977927,
%W A002427 -23749461029,8615841276005,-84802531453387,90219075042845,-26315271553053477373,
%X A002427 38089920879940267,-261082718496449122051,1520097643918070802691
%N A002427 Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
%C A002427 Doubled a(n+2)=-1,1,-3,5,-691,35, "gives" A140351(n+4) secondary Bernoulli 
               twin numbers.Thanks to Richard Mathar. [From Paul Curtz (bpcrtz(AT)free.fr), 
               Nov 28 2009]
%D A002427 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002427 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002427 L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, 
               reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 
               15, p. 93.
%D A002427 A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index 
               of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford 
               and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
%D A002427 M. Kaneko, "A recurrence formula for the Bernoulli numbers", Proc. Japan 
               Acad., 71 A (1995), 192-193.
%H A002427 T. D. Noe, <a href="b002427.txt">Table of n, a(n) for n=0..100</a>
%H A002427 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%e A002427 (n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 
               0, 5/66, ...
%t A002427 Numerator[ Table[2(2n + 1)BernoulliB[2n], {n, 1, 21}]]
%Y A002427 Denominators are in A006955. Cf. A050925/A050932, A000367/A002445.
%Y A002427 Sequence in context: A087368 A087670 A138584 this_sequence A136134 A119497 
               A012783
%Y A002427 Adjacent sequences: A002424 A002425 A002426 this_sequence A002428 A002429 
               A002430
%K A002427 sign,easy,nice,frac,new
%O A002427 0,5
%A A002427 N. J. A. Sloane (njas(AT)research.att.com).

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