OFFSET
0,5
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).
Francesca Aicardi, Catalan triangle and tied arc diagrams, arXiv:2011.14628 [math.CO], 2020.
Francesca Aicardi, Fuss-Catalan Triangles, arXiv:2310.07317 [math.CO], 2023.
EXAMPLE
Triangle begins:
1;
1, 0;
1, 3, 0;
1, 6, 15, 0;
1, 9, 39, 91, 0;
1, 12, 72, 272, 612, 0;
...
MATHEMATICA
A339350[n_, k_] := A339350[n, k] = Which[k == 0, 1, n == k, 0, True, Sum[Binomial[k-j+2, 2]*A339350[n-1, j], {j, 0, k}]];
Table[A339350[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Feb 23 2024 *)
PROG
(PARI) T(n, k) = if ((n==0) && (k==0), 1, if (n<=k, 0, sum(j=0, k, binomial(k-j+2, 2)*T(n-1, j))));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Dec 01 2020
STATUS
approved