A098509 Denominators of the inverse of a Catalan scaled binomial matrix.
1, 1, 1, 2, 1, 2, 5, 5, 5, 5, 14, 7, 7, 7, 14, 42, 42, 21, 21, 42, 42, 132, 22, 44, 33, 44, 22, 132, 429, 429, 143, 429, 429, 143, 429, 429, 1430, 715, 715, 715, 143, 715, 715, 715, 1430, 4862, 4862, 2431, 2431, 2431, 2431, 2431, 2431, 4862, 4862, 16796, 8398
Offset: 0
Examples
Rows begin 1; 1,1; 2,1,2; 5,5,5,5; 14,7,7,7,14; ...
Programs
-
Mathematica
T[n_, k_] := Denominator[(n + 1)*(Binomial[n, k]/Binomial[2*n, n])]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 07 2018 *)
Formula
Triangle T(n, k)=denominator((n+1)binomial(n, k)/binomial(2n, n))
Comments