[seqfan] Re: Tip about the triangle of Narayana numbers (A001263)

[M. F. Hasler]

On Tue, Apr 26, 2022 at 3:02 AM <urusenar at hotmail.com> wrote:

> Hello seqfans. This mail is about Narayana numbers (A001263).
> (...)

Another question about this numbers: if we only consider the left side of
> the Narayana triangle, is it possible 105 is the only repeated number in
> the triangle, excepting 1 (because are the row extrems)? I think yes but I
> cannot prove it because my Math level is too low.
>

No, 105 is not the only multiply repeated term > 1,
for example, 1176 and 4950 and 5713890 etc. also occur multiple times --
actually, any T(n,k) with  2 < k < n-1  which is a triangular number
m(m-1)/2  will occur later as  T(m,2) = T(m,m-1).

- Maximilian