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

urusenar at hotmail.com urusenar at hotmail.com
Mon Apr 25 19:50:27 CEST 2022

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

I've noticed that the Adamson comment about an operation to find the n-th row elements can be written by the following formula:

N(n,k) = N(n,k-1) * N(n-k+2,2) / N(k,2), for n>=k>=2.

I don't know if this formula is been already discovered or commented in the website, but perhaps the community considers this expresion useful to publish it. I have the proof, if someone needs it.

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.

Thank you for your time.

Best regards,

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