[seqfan] Wrong terms or wrong name in A046988?
Vladimir Reshetnikov
v.reshetnikov at gmail.com
Sat Mar 4 00:21:39 CET 2017
Dear SeqFans,
The name of the sequence A046988 contains two definitions: "Numerators of
Taylor series expansion of log(x/sin(x)). For n>0, numerators of
zeta(2*n)/Pi^(2*n)."
Presumably, it was intended that these definitions are consistent. But they
are not.
The first definition results in the sequence: 1, 1, 1, 1, 1, 691, 2, 3617,
43867, 174611, 155366, 236364091, 1315862, 3392780147, 6892673020804,
7709321041217, 151628697551, 26315271553053477373, 308420411983322,
261082718496449122051, 3040195287836141605382, 2530297234481911294093, ...
And the second: 1, 1, 1, 1, 1, 691, 2, 3617, 43867, 174611, 155366,
236364091, 1315862, 6785560294, 6892673020804, 7709321041217,
151628697551, 26315271553053477373, 308420411983322,
261082718496449122051, 3040195287836141605382, 5060594468963822588186, ...
These sequences are similar, but disagree at indexes 14, 22, 26, 28, 30,
38, 42, 44, 46, 50, 52, 54, 56, 58, 60, 62, 70, 74, 76, 78, 82, 84, 86,
88, 90, 92, 94, 98, 100, ...
The terms listed in A046988 agree with the second definition. Should we
remove the first part of the name in A046988, and submit is as a new
sequence? What should we do with the leading 0 term?
--
Thanks
Vladimir
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