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A155586 A modified Catalan sequence array. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A099940 A157249 A343233 * A069739 A066060 A008550

Adjacent sequences:  A155583 A155584 A155585 * A155587 A155588 A155589

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 24 2009

STATUS

approved

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Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)