[seqfan] Re: A question of Sloane and a possible bug. (A123854, A088802, A006934)

[Max Alekseyev]

A bit off-topic, but A088802 messes up what is conjectured and what is known.
First, it asks "Is this the same sequence as A123854?" and then gives
a PARI code that in fact implements formula for A123854.
If it's an open question, the code should be removed, or the two
sequences should be stated as duplicates.

Regards,
Max

On Sat, Mar 22, 2014 at 7:20 PM, Peter Luschny <peter.luschny at gmail.com> wrote:
> I have nothing to offer than to repeat a question Neil
> posed in A123854 and in A088802: are these the same
> sequences? Michael Somos thinks they are 'almost certainly'.
> And so do I.
>
> The reason I ask is another sequence: A006934. For me it
> looks as if A006934(7) is not correct. But this sequence is
> not easy to check.
>
> Now how do these two things relate to one another?
> By this rational sequence, based on some non-standard
> Bernoulli polynomials:
>
> 1, 1/4, 21/32, 671/128, 180323/2048, 20898423/8192, ...
>
> My conjecture is: the numerators of this seq are A006934
> and the denominators A123854 and/or A088802. If true,
> than the sequences can be computed by the Maple program
> given below.
>
> Perhaps someone can shade some light on these questions?
>
> Peter
>
> what_is_this := proc(n) local k, bp;
> bp := proc(n,x) option remember; local k;
> if n = 0 then 1 else -2*x*add(binomial(n-1,2*k+1)*
> bernoulli(2*k+2)/(2*k+2)*bp(n-2*k-2,x),k=0..n/2-1) fi end:
> add(bp(2*k,1/4)*(4*k)!/(2*k)!^2*x^(2*k),k=0..n-1);
> seq(((-1)^k*(coeff(%,x,2*k))),k=0..n-1) end:
> what_is_this(8);
>
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