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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
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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;
...
Contribution from Mats Granvik (mats.granvik(AT)abo.fi), Dec 18 2009: (Start)
The numbers in this triangle are sums of the following recursive number blocks:
1................................
.................................
11.....12........................
.................................
111....112....123................
.......122.......................
.................................
1111...1112...1123...1234........
.......1122...1223...............
.......1222...1233...............
.................................
11111..11112..11123..11234..12345
.......11122..11223..12234.......
.......11222..12223..12334.......
.......12222..11233..12344.......
..............12233..............
..............12333..............
.................................
(End)
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MAPLE
| 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
| Cf. A001793.
Sequence in context: A166994 A059083 A124931 * A194232 A110042 A123027
Adjacent sequences: A124929 A124930 A124931 * A124933 A124934 A124935
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2006
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