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Search: id:A120258
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| A120258 |
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Triangle of central coefficients of generalized Pascal-Narayana triangles. |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 20, 20, 4, 1, 1, 70, 175, 50, 5, 1, 1, 252, 1764, 980, 105, 6, 1, 1, 924, 19404, 24696, 4116, 196, 7, 1, 1, 3432, 226512, 731808, 232848, 14112, 336, 8, 1, 1, 12870, 2760615, 24293412, 16818516, 1646568, 41580, 540, 9, 1, 1, 48620
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Columns are the central coefficients of the triangles T(n, k;r) with T(n, k;r)=Product{j=0..r, C(n+j, k+j)/C(n-k+j, j)}*[k<=n]; (r=0,A007318), (r=1;A001263),(r=2,A056939),(r=3,A056940),(r=4,A056941). Essentially A103905 as a number triangle with an extra diagonal of 1's. Central coefficients T(2n, n) are A008793. Row sums are A120259. Diagonal sums are A120260.
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FORMULA
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Number triangle T(n, k)=[k<=n]*Product{j=0..k-1, C(2n-2k+j, n-k)/C(n-k+j, j)}
As a square array, this is T(n,m)=product{k=1..m, product{j=1..n, product{i=1..n, (i+j+k-1)/(i+j+k-2)}}}; - Paul Barry (pbarry(AT)wit.ie), May 13 2008
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EXAMPLE
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Triangle begins
1,
1, 1,
1, 2, 1,
1, 6, 3, 1,
1, 20, 20, 4, 1,
1, 70, 175, 50, 5, 1,
1, 252, 1764, 980, 105, 6, 1,
1, 924, 19404, 24696, 4116, 196, 7, 1
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CROSSREFS
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Cf. A120257.
Sequence in context: A112477 A156984 A084268 this_sequence A144351 A142589 A158389
Adjacent sequences: A120255 A120256 A120257 this_sequence A120259 A120260 A120261
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jun 13 2006
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