[seqfan] Delannoy numbers

mathcurves mathcurves at gmail.com
Wed May 20 14:13:47 CEST 2020


Hello seqfans,

I recently worked on the French page of delannoy numbers 
https://fr.wikipedia.org/wiki/Nombre_de_Delannoy, and suggest 
corrections on the corresponding page oeis

1) it should be said that T (n, k) = D (n-k, k) because it is not clear

2) D(n-k,k) is the number of lattice paths from (0,0) to (n,k) using 
steps (1,0), (0,1), (1,1). - Joerg Arndt 
<https://oeis.org/wiki/User:Joerg_Arndt>, Jul 01 2011
should be corrected into
D(n,k) is the number of lattice paths from (0,0) to (n,k) using steps 
(1,0), (0,1), (1,1). (or D(i,j) because the entry says D(i,j) ?)

3) "Sum of n-th row = A000129 <https://oeis.org/A000129>(n). - Reinhard 
Zumkeller <https://oeis.org/wiki/User:Reinhard_Zumkeller>, Dec 03 2004 
"  and  "Row sums are A000129 <https://oeis.org/A000129>. - Roger L. 
Bagula <https://oeis.org/wiki/User:Roger_L._Bagula>, Dec 09 2008 "   are 
exactly the same and more precisely, it should be said :
Sum_{k=0..n} D(n-k,k) = Sum_{k=0..n} T(n,k) = A000129 
<https://oeis.org/A000129>(n+1) (because A000129 
<https://oeis.org/A000129>(0)=0 not 1 )

Best regards




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