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A120257
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Triangle of Hankel transforms of certain binomial sums.
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1
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1, 2, -1, 3, -6, -1, 4, -20, -20, 1, 5, -50, -175, 70, 1, 6, -105, -980, 1764, 252, -1, 7, -196, -4116, 24696, 19404, -924, -1, 8, -336, -14112, 232848, 731808, -226512, -3432, 1, 9, -540, -41580, 1646568, 16818516, -24293412, -2760615, 12870, 1, 10, -825, -108900, 9343620, 267227532, -1447482465
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row k is the Hankel transform of sum{j=0..n, C(k+j, j)}. Absolute value is reversal of A103905. Diagonal and sub-diagonals are essentially signed versions of the central coefficients of certain generalized Pascal-Narayana triangles (A007318, A001263, A056939, A056940, A056941).
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FORMULA
| T(n, k):=(cos(pi*k/2)-sin(pi*k/2))*product{j=0..n-k-1, C(2k+2+j, k+1)/C(k+1+j, j)}
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EXAMPLE
| Triangle begins
1,
2, -1,
3, -6, -1,
4, -20, -20, 1,
5, -50, -175, 70, 1,
6, -105, -980, 1764, 252, -1,
7, -196, -4116, 24696, 19404, -924, -1,
8, -336, -14112, 232848, 731808, -226512, -3432, 1
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CROSSREFS
| Cf. A120258.
Sequence in context: A093346 A115597 A103371 * A059298 A156914 A059434
Adjacent sequences: A120254 A120255 A120256 * A120258 A120259 A120260
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 13 2006
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