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

0,8

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)

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A107333 A161642 A152141 * A178395 A330958 A327186

Adjacent sequences: A098502 A098503 A098504 * A098506 A098507 A098508

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 11 2004

Status

approved