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A141432
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Triangle T(n,k) = (k+1)*(n-k-1) read by rows.
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1
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-2, 0, -3, 2, 0, -4, 4, 3, 0, -5, 6, 6, 4, 0, -6, 8, 9, 8, 5, 0, -7, 10, 12, 12, 10, 6, 0, -8, 12, 15, 16, 15, 12, 7, 0, -9, 14, 18, 20, 20, 18, 14, 8, 0, -10, 16, 21, 24, 25, 24, 21, 16, 9, 0, -11
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OFFSET
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1,1
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LINKS
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FORMULA
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T(n,k) = (k+1)*(n-k-1).
Sum_{k=1..n} T(n, k) = n*(n^2 - 13)/6.
G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = (2*x-1-y)/((1-y)^3*(x-1)^2). - R. J. Mathar, Feb 19 2020
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EXAMPLE
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Triangle begins as:
-2;
0, -3;
2, 0, -4;
4, 3, 0, -5;
6, 6, 4, 0, -6;
8, 9, 8, 5, 0, -7;
10, 12, 12, 10, 6, 0, -8;
12, 15, 16, 15, 12, 7, 0, -9;
14, 18, 20, 20, 18, 14, 8, 0, -10;
16, 21, 24, 25, 24, 21, 16, 9, 0, -11;
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MAPLE
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MATHEMATICA
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Table[(k+1)*(n-k-1), {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 01 2021 *)
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PROG
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(Magma) [(k+1)*(n-k-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 01 2021
(Sage) flatten([[(k+1)*(n-k-1) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 01 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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