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Search: id:A124847
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| A124847 |
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Triangle read by rows: T(n,k)=k(k+1)binom(n-1,k-1)/2 (1<=k<=n). |
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1
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| 1, 1, 3, 1, 6, 6, 1, 9, 18, 10, 1, 12, 36, 40, 15, 1, 15, 60, 100, 75, 21, 1, 18, 90, 200, 225, 126, 28, 1, 21, 126, 350, 525, 441, 196, 36, 1, 24, 168, 560, 1050, 1176, 784, 288, 45, 1, 27, 216, 840, 1890, 2646, 2352, 1296, 405, 55, 1, 30, 270, 1200, 3150, 5292, 5880
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums = A049611: (1, 4, 13, 38, 104... Binomial transform of (1, 3, 6...) = A049611: (1, 4, 13, 38...).
Triangle is P*A, where P is the Pascal triangle written as a lower triangular matrix and C is the diagonal matrix of the triangular numbers 1,3,6,10,....
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EXAMPLE
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First few rows of the triangle are:
1;
1, 3;
1, 6, 6;
1, 9, 18, 10;
1, 12, 36, 40, 15;
1, 15, 60, 100, 75, 21;
...
Sum of row 3 = 38 = (1 + 9 + 18 + 10), where 38 = A049611(3).
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MAPLE
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T:=(n, k)->k*(k+1)*binomial(n-1, k-1)/2: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A049611.
Sequence in context: A112351 A109954 A133545 this_sequence A127893 A127895 A116412
Adjacent sequences: A124844 A124845 A124846 this_sequence A124848 A124849 A124850
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 10 2006
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EXTENSIONS
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Edited by njas, Nov 24 2006
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