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A131427 A000108(n) preceded by n zeros. 6
1, 0, 1, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 429, 0, 0, 0, 0, 0, 0, 0, 0, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58786, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208012 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Triangle given by A000004 DELTA A000012 where DELTA is the operator defined in A084938. - Philippe Deléham, Jul 12 2007

T(n,k) is the number of Dyck paths of semilength n having exactly k U=(1,1) steps. - Alois P. Heinz, Jun 09 2014

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

FORMULA

A000108(n) preceded by n zeros, as an infinite lower triangular matrix.

EXAMPLE

First few rows of the triangle are:

1;

0, 1;

0, 0, 2;

0, 0, 0, 5;

0, 0, 0, 0, 14;

0, 0, 0, 0, 0, 42;

...

MAPLE

T:= (n, k)-> `if`(k<n, 0, binomial(2*n, n)/(n+1)):

seq(seq(T(n, k), k=0..n), n=0..15);  # Alois P. Heinz, Jun 09 2014

MATHEMATICA

T[n_, n_] := CatalanNumber[n]; T[_, _] = 0;

Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 20 2016 *)

CROSSREFS

Cf. A131428, A131429, A000108, A243752.

Sequence in context: A328820 A259863 A283666 * A153198 A182492 A222898

Adjacent sequences:  A131424 A131425 A131426 * A131428 A131429 A131430

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jul 10 2007

EXTENSIONS

More terms from Philippe Deléham, Oct 16 2008

STATUS

approved

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Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)