OFFSET
0,5
LINKS
William Linz, s-Catalan numbers and Littlewood-Richardson polynomials, arXiv:2110.12095 [math.CO], 2021. See p. 2.
FORMULA
A(n, s) = T(2*n, s*n, s), where T(n, k, s) is the s-binomial coefficient defined as the coefficient of x^k in (Sum_{i=0..s} x^i)^n.
EXAMPLE
The array begins:
n\s | 0 1 2 3 4
----+----------------------------
0 | 1 1 1 1 1 ...
1 | 1 2 3 4 5 ...
2 | 1 6 19 44 85 ...
3 | 1 20 141 580 1751 ...
4 | 1 70 1107 8092 38165 ...
...
MATHEMATICA
T[n_, k_, s_]:=If[k==0, 1, Coefficient[(Sum[x^i, {i, 0, s}])^n, x^k]]; A[n_, s_]:=T[2n, s n, s]; Flatten[Table[A[n-s, s], {n, 0, 9}, {s, 0, n}]]
CROSSREFS
KEYWORD
AUTHOR
Stefano Spezia, Dec 06 2021
STATUS
approved