A155586 A modified Catalan sequence array.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 2, 1, 1, 1, 14, 5, 2, 1, 1, 1, 42, 14, 5, 2, 1, 1, 1, 132, 42, 14, 5, 2, 1, 1, 1, 429, 132, 42, 14, 5, 2, 1, 1, 1, 1430, 429, 132, 42, 14, 5, 2, 1, 1, 1, 4862, 1430, 429, 132, 42, 14, 5, 2, 1, 1, 1, 16796, 4862, 1430, 429, 132, 42, 14, 5, 2, 1, 1

Offset: 0

Author

Paul Barry, Jan 24 2009

Keywords

• easy
• nonn
• tabl

Comments

Row sums are in A155587. Stieltjes associate array to A091491.

Examples

			Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins
  1;
  1,    1;
  1,    1,   1;
  1,    2,   1,   1;
  1,    5,   2,   1,  1;
  1,   14,   5,   2,  1,  1;
  1,   42,  14,   5,  2,  1, 1;
  1,  132,  42,  14,  5,  2, 1, 1;
  1,  429, 132,  42, 14,  5, 2, 1, 1;
  1, 1430, 429, 132, 42, 14, 5, 2, 1, 1;
  ...
		

Crossrefs

Cf. A000108, A091491, A155587.

Formula

T(n,k) = [k <= n] * if(k=0, 1, A000108(n-k)) for 0 <= k <= n, where [ ] is the Iverson bracket.

Bivariate o.g.f.: 1/(1 - x) + c(x) * x*y/(1 - x*y), where c(x) is the o.g.f. of A000108. - Petros Hadjicostas, Aug 03 2020