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A120258
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Triangle of central coefficients of generalized Pascal-Narayana triangles.
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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| 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
| 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
| Cf. A120257.
Sequence in context: A181621 A084268 A201198 * A201922 A181644 A144351
Adjacent sequences: A120255 A120256 A120257 * A120259 A120260 A120261
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 13 2006
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