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A141681
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The matrix inverse of the triangle A141680.
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1
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1, -4, 1, -9, 0, 1, 32, -12, 0, 1, -25, 0, 0, 0, 1, 504, -45, -40, 0, 0, 1, -49, 0, 0, 0, 0, 0, 1, -4096, 1568, 0, -140, 0, 0, 0, 1, 2187, 0, -252, 0, 0, 0, 0, 0, 1, 13400, -225, 0, 0, -504, 0, 0, 0, 0, 1, -121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
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refs;
listen;
history;
text;
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OFFSET
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1,2
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COMMENTS
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Row sums are 1, -3, -8, 21, -24, 420, -48, -2667, 1936, 12672, ...
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LINKS
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FORMULA
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Sum_{j=k..n} T(n,j) * A141680(j,k) = delta(n,k).
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EXAMPLE
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Triangle begins
1;
-4, 1;
-9, 0, 1;
32, -12, 0, 1;
-25, 0, 0, 0, 1;
504, -45, -40, 0, 0, 1;
-49, 0, 0, 0, 0, 0, 1;
-4096, 1568, 0, -140, 0, 0, 0, 1;
2187, 0, -252, 0, 0, 0, 0, 0, 1;
13400, -225, 0, 0, -504, 0, 0, 0, 0, 1;
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MATHEMATICA
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t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]*Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]; Table[Sum[t[n, m], {m, 1, n}], {n, 1, 10}]; M = Inverse[Table[Table[t[n, m], {m, 1, 10}], {n, 1, 10}]]; Table[Table[M[[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[%]
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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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