[seqfan] Re: Conjecture about A127750

[Richard J. Mathar]

The recurrence of a row in A127749 is right-to-left
A127749(n,n) = 2*n+1
A127749(n,k) = -(2*k+1) *sum_{i=k+1... min(n,2*k)) A127749(n,i)/(2*i+1)., k<n.
The recurrence means to "undo" the multiplication of the odd'ed index
of the elements "right from" k, accumulate, and multiply back-in the (2*k+1).
>From this I'd conclude that A127749(n,k) = (2*k+1)*A111967(n,k),
because A111967 is doing the same without the re-weighting by the
odd integers. So the conjecture in A127750 is equivalent to the
conjecture in A111967.