OFFSET
0,3
COMMENTS
Same as A336524 with the main diagonal removed.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).
Cyril Banderier, Philippe Marchal, and Michael Wallner, Rectangular Young tableaux with local decreases and the density method for uniform random generation (short version), arXiv:1805.09017 [cs.DM], 2018.
FORMULA
T(n, k) = 1/(n + 1 - k)*binomial(n, k)*binomial(2*n, n).
G.f.: (sqrt(1 - 4*x*y) - sqrt(1 - 4*x*(1 + y)))/(2*x). - Stefano Spezia, Feb 04 2024
EXAMPLE
Triangle T(n, k) begins:
1,
1, 2,
2, 6, 6,
5, 20, 30, 20,
14, 70, 140, 140, 70,
42, 252, 630, 840, 630, 252,
132, 924, 2772, 4620, 4620, 2772, 924,
429, 3432, 12012, 24024, 30030, 24024, 12012, 3432,
MAPLE
MATHEMATICA
A368745row[n_] := Binomial[n, #]*Binomial[2*n, n]/(n+1-#) & [Range[0, n]];
Array[A368745row, 10, 0] (* Paolo Xausa, Feb 27 2024 *)
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Feb 04 2024
STATUS
approved