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

0,4

Comments

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

Links

Table of n, a(n) for n=0..56.

Formula

Triangle T(n, k)=denominator((n+1)binomial(n, k)/binomial(2n, n))

Example

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

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 *)

Crossrefs

Cf. A098505, A098474.

Sequence in context: A241349 A330405 A111934 * A019910 A084309 A047991

Adjacent sequences: A098506 A098507 A098508 * A098510 A098511 A098512

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 11 2004

Status

approved