Search: id:A117972
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%I A117972
%S A117972 1,1,3,45,315,14175,467775,42567525,638512875,97692469875,9280784638125,
%T A117972 2143861251406875,147926426347074375,48076088562799171875,
%U A117972 9086380738369043484375,3952575621190533915703125
%V A117972 1,-1,3,-45,315,-14175,467775,-42567525,638512875,-97692469875,9280784638125,
%W A117972 -2143861251406875,147926426347074375,-48076088562799171875,9086380738369043484375,
%X A117972 -3952575621190533915703125
%N A117972 Numerator of Zeta'[ -2n].
%C A117972 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%C A117972 In A160464 the coefficients of the ES1 matrix are defined. This matrix 
               led to the discovery that the successive differences of the ES1[1-2*m,
               n] coefficients for m= 1, 2, 3, .. , are equal to the values of Zeta'[ 
               -2n], see also A094665 and A160468.
%C A117972 (End)
%H A117972 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RiemannZetaFunction.html">Riemann Zeta Function</a>
%e A117972 -1/4, 3/4, -45/8, 315/4, -14175/8, 467775/8, -42567525/16, ...
%e A117972 -Zeta[3]/(4*Pi^2), (3*Zeta[5])/(4*Pi^4), (-45*Zeta[7])/(8*Pi^6), (315*Zeta[9])/
               (4*Pi^8), (-14175*Zeta[11])/(8*Pi^10), ...
%p A117972 Contribution from Peter Luschny (peter(AT)luschny.de), May 02 2009: (Start)
%p A117972 # Without rational arithmetic
%p A117972 a := n -> (-1)^n*(2*n)!*2^(add(i,i=convert(n,base,2))-2*n); (End)
%t A117972 Numerator[(2*n)!/2^(2*n + 1)(-1)^n]
%Y A117972 Cf. A117973.
%Y A117972 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A117972 Cf. A160464, A094665 and A160468.
%Y A117972 Absolute values equal row sums of A160468.
%Y A117972 (End)
%Y A117972 Sequence in context: A062346 A002682 A073595 this_sequence A061532 A060242 
               A141445
%Y A117972 Adjacent sequences: A117969 A117970 A117971 this_sequence A117973 A117974 
               A117975
%K A117972 sign,frac
%O A117972 0,3
%A A117972 Eric Weisstein (eric(AT)weisstein.com), Apr 06, 2006
%E A117972 First term added, offset changed and edited by Johannes W. Meijer (meijgia(AT)hotmail.com), 
               May 15 2009

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