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A248473
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Triangle of numbers b(i,j) = A(binomial(A(i), A(j))), where A = A007913, with the convention that A(0)=0.
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2
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 0, 0, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 5, 6, 6, 1, 1, 7, 21, 35, 7, 21, 7, 1, 1, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 10, 5, 30, 10, 7, 210, 30, 5, 10, 1, 1, 11, 55, 165, 11, 462, 462, 330, 55, 11, 11, 1
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OFFSET
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0,5
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COMMENTS
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By definition, all terms are squarefree (A005117).
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LINKS
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EXAMPLE
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For i=8, j=4, we have A(8)=2, A(4)=1, hence b(8,4) = A(binomial(2,1)) = 2.
Triangle begins
1
1 1
1 2 1
1 3 3 1
1 1 0 0 1
1 5 10 10 5 1
1 6 15 5 6 6 1
1 7 21 35 7 21 7 1
1 2 1 0 2 0 0 0 1
1 1 0 0 1 0 0 0 0 1
1 10 5 30 10 7 210 30 5 10 1
..........................................
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MATHEMATICA
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a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]], 2])&[Transpose[FactorInteger[n]]];
Flatten[Table[a7913[Binomial[a7913[m], a7913[k]]], {m, 0, 10}, {k, 0, m}]] (* Peter J. C. Moses, Oct 27 2014 *)
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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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