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%I #18 Jan 14 2015 11:17:32
%S 1,2,1,2,-1,-1,1,4,-3,-25,5,1382,-691,-49,35,28936,-3617,-131601,
%T 43867,349222,-1222277,-9399643,854513,945456364,-1181820455,
%U -111190339,76977927,332492454406,-23749461029,-43079206380025,8615841276005
%N Numerators of the image of the Akiyama-Tanigawa transform applied to the second Bernoulli numbers.
%C Start from a row of modified Bernoulli numbers A164555(k)/A027642(k), namely,
%C 1/1, 1/2, 1/6, 0/1, -1/30, 0/1, 1/42, 0/1, -1/30, ... .
%C Applying the Takiyama-Tanigawa transformation to this sequence results in
%C 1/2, 2/3, 1/2, 2/15, -1/6, -1/7, 1/6, 4/15, -3/10, -25/33, 5/6, ... .
%C The current sequence contains the numerators of this image of the transform.
%H D. Merlini, R. Sprugnoli, M. C. Verri, <a href="http://www.emis.de/journals/INTEGERS/papers/f5/f5.Abstract.html">The Akiyama-Tanigawa Transformation</a>, Integers, 5 (1) (2005) #A05
%t b[0]=0; b[1]=1; b[2]=1/2; b[n_] := BernoulliB[n-1]; a[0, m_] := b[m+1]; a[n_, m_] := a[n, m] = (m+1)*(a[n-1, m] - a[n-1, m+1]); Table[a[1, m], {m, 0, 30}] // Numerator (* _Jean-François Alcover_, Aug 09 2012 *)
%K sign,frac
%O 0,2
%A _Paul Curtz_, Mar 08 2010
%E Values corrected by Lisa Schreiber (lisa.schreiber(AT)uni-jena.de), Jul 14 2010
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