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

0,8

Comments

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

Links

Table of n, a(n) for n=0..77.

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

Example

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.

Sequence in context: A157249 A351861 A343233 * A069739 A066060 A008550

Adjacent sequences: A155583 A155584 A155585 * A155587 A155588 A155589

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 24 2009

Status

approved