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

[Peter Luschny]

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);