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Search: id:A124932
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| A124932 |
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Triangle read by rows: T(n,k)=k(k+1)binom(n,k)/2 (1<=k<=n). |
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+0
1
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| 1, 2, 3, 3, 9, 6, 4, 18, 24, 10, 5, 30, 60, 50, 15, 6, 45, 120, 150, 90, 21, 7, 63, 210, 350, 315, 147, 28, 8, 84, 336, 700, 840, 588, 224, 36, 9, 108, 504, 1260, 1890, 1764, 1008, 324, 45, 10, 135, 720, 2100, 3780, 4410, 3360, 1620, 450, 55, 11, 165, 990, 3300, 6930
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums = A001793: (1, 5, 18, 56, 160, 432...).
Triangle is P*M, where P is the Pascal triangle as an infinite lower triangular matrix and M is an infinite bidiagonal matrix with (1,3,6,10,...) in the main diagonal and in the subdiagonal.
This number triangle can be used as a control sequence when listing combinations of subsets as in Pascals triangle by assigning a number to each element that corresponds to the n:th subset that the element belongs to. One then gets number blocks whose sums are the terms in this number triangle. [From Mats Granvik (mats.granvik(AT)abo.fi), Jan 14 2009]
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EXAMPLE
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First few rows of the triangle are:
1;
2, 3;
3, 9, 6;
4, 18, 24, 10;
5, 30, 60, 50, 15;
6, 45, 120, 150, 90, 21;
7, 63, 210, 350, 315, 147, 28;
...
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MAPLE
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T:=(n, k)->k*(k+1)*binomial(n, k)/2: for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001793.
Sequence in context: A157126 A059083 A124931 this_sequence A110042 A123027 A100652
Adjacent sequences: A124929 A124930 A124931 this_sequence A124933 A124934 A124935
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2006
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