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A052553
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Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by antidiagonals.
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9
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1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 6, 1, 0, 0, 0, 1, 6, 10, 4, 0, 0, 0, 0, 1, 7, 15, 10, 1, 0, 0, 0, 0, 1, 8, 21, 20, 5, 0, 0, 0, 0, 0, 1, 9, 28, 35, 15, 1, 0, 0, 0, 0, 0, 1, 10, 36, 56, 35, 6, 0, 0, 0, 0, 0, 0, 1, 11, 45, 84, 70, 21, 1, 0, 0, 0, 0, 0, 0, 1, 12, 55
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Another version of Pascal's triangle A007318.
As a triangle read by rows, it is (1,0,0,0,0,0,0,0,0,...) DELTA (0,1,-1,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938 and it is the Riordan array (1/(1-x), x^2/(1-x)). The row sums of this triangle are F(n+1) = A000045(n+1). - DELEHAM Philippe, Dec 11 2011
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LINKS
| Index entries for triangles and arrays related to Pascal's triangle
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FORMULA
| As a triangle : T(n,k) = A026729(n,n-k).
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EXAMPLE
| Array begins:
1 0 0 0 0 0 ...
1 1 0 0 0 0 ...
1 2 1 0 0 0 ...
1 3 3 1 0 0 ...
1 4 6 4 1 0 ...
1 5 10 10 5 1 ...
with(combinat): for s from 0 to 20 do for n from s to 0 by -1 do printf(`%d,`, binomial(n, s-n)) od:od:
As a triangle, this begins :
1
1, 0
1, 1, 0
1, 2, 0, 0
1, 3, 1, 0, 0
1, 4, 3, 0, 0, 0
1, 5, 6, 1, 0, 0, 0
1, 6, 10, 4, 0, 0, 0, 0
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CROSSREFS
| The official entry for Pascal's triangle is A007318. See also A026729.
Cf. A052509, A054123, A054124, A008949.
Sequence in context: A029362 A114510 A077029 * A045847 A137586 A175045
Adjacent sequences: A052550 A052551 A052552 * A052554 A052555 A052556
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KEYWORD
| nonn,tabl,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 17 2000
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EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 17 2000
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