A098505 Numerators in inverse of a Catalan scaled binomial matrix.

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 3, 2, 1, 1, 5, 5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1, 7, 7, 35, 35, 7, 7, 1, 1, 4, 14, 28, 7, 28, 14, 4, 1, 1, 9, 18, 42, 63, 63, 42, 18, 9, 1, 1, 5, 45, 30, 105, 63, 105, 30, 45, 5, 1, 1, 11, 55, 165, 165, 33, 33, 165, 165, 55, 11, 1, 1, 3, 33, 55, 495, 198

Offset: 0

Author

Paul Barry, Sep 11 2004

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A098506. Diagonal sums are A098507. Second column is A093527. Third column is A098508. Numerators in the inverse of the signed version of A098474, defined by T(n,k)=(-1)^(n-k)binomial(2k,k)binomial(n,k)/(k+1)

Examples

			Rows begin:
  1;
  1,1;
  1,1,1;
  1,3,3,1;
  1,2,3,2,1;
  1,5,5,5,5,1;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).

Crossrefs

Cf. A098474, A098506, A098507, A098508, A093527.

Programs

Mathematica

Table[Numerator[(n + 1)*Binomial[n, k]/Binomial[2*n, n]], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Aug 30 2024 *)

Formula

T(n, k) = numerator((n+1)*binomial(n, k)/binomial(2n, n)).