[seqfan] Re: Wrong terms or wrong name in A046988?
Vladimir Reshetnikov
v.reshetnikov at gmail.com
Sun Mar 5 22:51:48 CET 2017
The Comtet reference is correct. As I mentioned in comments for A283301,
the sequence A046988 are the numerators of
2^(2*n-1)*(-1)^(n+1)*Bernoulli(2*n)/(2*n)!, and A283301 are the numerators
of 2^(2*n-1)*(-1)^(n+1)*Bernoulli(2*n)/(n*(2*n)!). Note the additional
factor 1/n in the latter. For some values of n there occurs a cancellation
of common factors, so numerators are different by those factors. For n <
9000, the factors are only powers of two: 2, 4, 8, 16, 32. I'm not sure if
there other factors for higher n.
--
Vladimir
On Sun, Mar 5, 2017 at 12:05 AM, Frank Adams-Watters <franktaw at netscape.net>
wrote:
> Are my posts to seqfan not getting through?
>
> The two sequences are the same; the Comtet reference (and likely some of
> the other references, but that's the one I could check) shows this. The
> discrepancy is almost certainly the result of a rounding error of some sort.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Vladimir Reshetnikov <v.reshetnikov at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Sun, Mar 5, 2017 1:14 am
> Subject: [seqfan] Re: Wrong terms or wrong name in A046988?
>
> See proposed changes to sequences A046988, A046989 and A283301 (new).
> --ThanksVladimir
>
> On Sat, Mar 4, 2017 at 1:26 AM, C Boyd <cb1 at gmx.co.uk> wrote
> :>> Dear Seqfans,>> I mentioned the problem with A046988 in a list
> exchange with
> > Robert Israel in early 2016:
> >> > (I suppose A046988 has to be revised. The simplest approach would
> > > be to create a direct counterpart to A002432 by re-titling it as
> > > "Numerators of zeta(2*n)/Pi^(2*n)", removing A046988(0), and
> > > changing the offset to 1. In addition, a new sequence called
> > > "Numerators of Taylor series expansion of log(x/sin(x))" could be
> > > created. Editors please advise.)
> >> See: http://list.seqfan.eu/pipermail/seqfan/2015-December/015906.html
> >> There can be subtle effects of cancelling in sequences involving
> > Bernoulli numbers.
> >> CB
> >> --> Seqfan Mailing list - http://list.seqfan.eu/
> >--Seqfan Mailing list - http://list.seqfan.eu/
>
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