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A127512
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Triangle read by rows: T(n,k)= mobius(n)*binomial(n-1,k-1).
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4
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1, -1, -1, -1, -2, -1, 0, 0, 0, 0, -1, -4, -6, -4, -1, 1, 5, 10, 10, 5, 1, -1, -6, -15, -20, -15, -6, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, -1, -10, -45, -120, -210, -252, -210, -120, -45, -10, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle:
1;
-1, -1;
-1, -2, -1;
0, 0, 0, 0;
-1, -4, -6, -4, -1;
1, 5, 10, 10, 5, 1;
...
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MAPLE
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numtheory[mobius](n)*binomial(n-1, k-1) ;
end proc:
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PROG
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(PARI) row(n) = my(M = matrix(n, n, i, j, if (i==j, moebius(i))), P = matrix(n, n, i, j, binomial(i-1, j-1))); vector(n, k, (M*P)[n, k]); \\ Michel Marcus, Feb 15 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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