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A097750
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Binomial transform of the Whitney triangle.
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1
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1, 1, 2, 1, 4, 4, 1, 6, 11, 8, 1, 8, 22, 26, 16, 1, 10, 37, 64, 57, 32, 1, 12, 56, 130, 163, 120, 64, 1, 14, 79, 232, 386, 382, 247, 128, 1, 16, 106, 378, 794, 1024, 848, 502, 256, 1, 18, 137, 576, 1471, 2380, 2510, 1816, 1013, 512, 1, 20, 172, 834, 2517, 4944, 6476, 5812
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| As a member of the Riordan group, this is (1/(1-2x), x/(1-x)^2). Row sums are A061667 and diagonal sums are A045623. The n-th row elements correspond to the end elements of the 2n-th row of the Whitney triangle A004070. Corresponds to the product of Pascal's triangle and the Whitney triangle.
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FORMULA
| Number triangle T(n, k)=sum{i=0..n, binomial(n+k, i-k)}
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EXAMPLE
| Rows begin {1}, {1,2}, {1,4,4}, {1,6,11,8} ...
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CROSSREFS
| Cf. A097761.
Sequence in context: A200057 A136600 A136672 * A133544 A013609 A154558
Adjacent sequences: A097747 A097748 A097749 * A097751 A097752 A097753
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 23 2004
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