Fuss-Catalan Triangles

Francesca Aicardi

Published 2023-10-11Version 1

For each $p>0$ we define by recurrence a triangle $T^p(n,k)$ whose rows sum to the Fuss-Catalan numbers $ \frac{1}{p n+1}\binom{pn+1}{n}$, generalizing the known Catalan triangle corresponding to the case $p=2$. The proof is given for $p=4$. Moreover, for some small values of $p$, the signed sums turn out to be known sequences.