# [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

```