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A130020 Triangle T(n,k), 0<=k<=n, read by rows given by [1,0,0,0,0,0,0,...] DELTA [0,1,1,1,1,1,1,...] where DELTA is the operator defined in A084938 . 18
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 5, 0, 1, 4, 9, 14, 14, 0, 1, 5, 14, 28, 42, 42, 0, 1, 6, 20, 48, 90, 132, 132, 0, 1, 7, 27, 75, 165, 297, 429, 429, 0, 1, 8, 35, 110, 275, 572, 1001, 1430, 1430, 0, 1, 9, 44, 154, 429, 1001, 2002, 3432, 4862, 4862, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Reflected version of A106566 .

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Sum_{k, 0<=k<=n}T(n,k)=A000108(n).

EXAMPLE

Triangle begins:

1;

1, 0;

1, 1, 0;

1, 2, 2, 0;

1, 3, 5, 5, 0;

1, 4, 9, 14, 14, 0;

1, 5, 14, 28, 42, 42, 0;

1, 6, 20, 48, 90, 132, 132, 0;

1, 7, 27, 75, 165, 297, 429, 429, 0;

1, 8, 35, 110, 275, 572, 1001, 1430, 1430, 0;

1, 9, 44, 154, 429, 1001, 2002, 3432, 4862, 4862, 0 ;...

PROG

(Sage)

@CachedFunction

def A130020(n, k):

    if n==k: return add((-1)^j*binomial(n, j) for j in (0..n))

    return add(A130020(n-1, j) for j in (0..k))

for n in (0..10) :

    [A130020(n, k) for k in (0..n)]  # Peter Luschny, Nov 14 2012

CROSSREFS

The following are all versions of (essentially) the same Catalan triangle: A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.

Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 A003519 A001392, ...

Sequence in context: A172236 A191646 A277938 * A292870 A091063 A246935

Adjacent sequences:  A130017 A130018 A130019 * A130021 A130022 A130023

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jun 16 2007

STATUS

approved

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Last modified December 12 16:38 EST 2017. Contains 295949 sequences.