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A182701
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Triangle T(n,k) = n*A000041(n-k) read by rows, 1 <= k <= n. Sum of the parts of all partitions of n that contain k as a part.
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8
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1, 2, 2, 6, 3, 3, 12, 8, 4, 4, 25, 15, 10, 5, 5, 42, 30, 18, 12, 6, 6, 77, 49, 35, 21, 14, 7, 7, 120, 88, 56, 40, 24, 16, 8, 8, 198, 135, 99, 63, 45, 27, 18, 9, 9, 300, 220, 150, 110, 70, 50, 30, 20, 10, 10, 462, 330, 242, 165, 121, 77, 55, 33, 22, 11, 11, 672, 504, 360, 264, 180, 132, 84, 60, 36, 24, 12, 12
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OFFSET
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1,2
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COMMENTS
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By definition, the entries in row n are divisible by n.
Row sums are 1, 4, 12, 28, 60, 114, ... = n*A000070(n).
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
2, 2;
6, 3, 3;
12, 8, 4, 4;
25, 15, 10, 5, 5;
42, 30, 18, 12, 6, 6;
77, 49, 35, 21, 14, 7, 7;
120, 88, 56, 40, 24, 16, 8, 8;
198, 135, 99, 63, 45, 27, 18, 9, 9;
300, 220, 150, 110, 70, 50, 30, 20, 10, 10;
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MAPLE
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A182701 := proc(n, k) n*combinat[numbpart](n-k) ; end proc:
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MATHEMATICA
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T[n_, k_] := n PartitionsP[n - k];
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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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