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

Author

Paul Barry, Sep 11 2004

Keywords

• easy
• nonn
• tabl

Comments

First column and main diagonal are A000108. Row sums are A098510. Diagonal sums are A098511. Second column is A098512.

Examples

			Rows begin
1;
1,1;
2,1,2;
5,5,5,5;
14,7,7,7,14;
...
		

Crossrefs

Cf. A098505, A098474.

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))