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A079904
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Triangle read by rows: T(n, k) = n*k, 0<=k<=n.
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4
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0, 0, 1, 0, 2, 4, 0, 3, 6, 9, 0, 4, 8, 12, 16, 0, 5, 10, 15, 20, 25, 0, 6, 12, 18, 24, 30, 36, 0, 7, 14, 21, 28, 35, 42, 49, 0, 8, 16, 24, 32, 40, 48, 56, 64, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121
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OFFSET
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0,5
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COMMENTS
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T(n, k) = if k=0 then 0 else T(n,k-1)+n;
T(n, 0)=1; T(n, 1)=n for n>0; T(n, 2)=A005843(n) for n>1; T(n, 3)=A008585(n) for n>2; T(n, 4)=A008586(n) for n>3;
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LINKS
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FORMULA
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T(n, k) = n*k, 0 <= k <= n.
G.f. as triangle: (1 + x*y - 2*x^2*y)*x*y/((1-x)^2*(1-x*y)^3).
G.f. as sequence: -Sum(n >= 0, (n^2-n)*x^(n*(n+1)/2))/(1-x) + Sum(n >= 1, x^(n*(n+1)/2)) * x/(1-x)^2. These sums are related to Jacobi Theta functions.
(End)
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EXAMPLE
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The triangle T(n, k) begins:
n\k 0 1 2 3 4 5 6 7 8 9 10 ...
0: 0
1: 0 1
2: 0 2 4
3: 0 3 6 9
4: 0 4 8 12 16
5: 0 5 10 15 20 25
6: 0 6 12 18 24 30 36
7: 0 7 14 21 28 35 42 49
8: 0 8 16 24 32 40 48 56 64
9: 0 9 18 27 36 45 54 63 72 81
10: 0 10 20 30 40 50 60 70 80 90 100
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MAPLE
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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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