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A207645
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Triangle where T(n,k) = Product_{j=1..k} floor(n/j - 1), as read by rows n>=0, columns k=0..[n/2].
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6
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1, 1, 1, 1, 1, 2, 1, 3, 3, 1, 4, 4, 1, 5, 10, 10, 1, 6, 12, 12, 1, 7, 21, 21, 21, 1, 8, 24, 48, 48, 1, 9, 36, 72, 72, 72, 1, 10, 40, 80, 80, 80, 1, 11, 55, 165, 330, 330, 330, 1, 12, 60, 180, 360, 360, 360, 1, 13, 78, 234, 468, 468, 468, 468, 1, 14, 84, 336, 672, 1344, 1344, 1344
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OFFSET
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0,6
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COMMENTS
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Compare the definition to that of Pascal's triangle:
binomial(n,k) = Product_{j=1..k} ((n+1)/j - 1).
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LINKS
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FORMULA
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Right border of even-indexed rows equals A207646.
Right border of odd-indexed rows equals A207647.
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EXAMPLE
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Triangle begins with row n=0 as:
1;
1;
1, 1;
1, 2;
1, 3, 3;
1, 4, 4;
1, 5, 10, 10;
1, 6, 12, 12;
1, 7, 21, 21, 21;
1, 8, 24, 48, 48;
1, 9, 36, 72, 72, 72;
1, 10, 40, 80, 80, 80;
1, 11, 55, 165, 330, 330, 330;
1, 12, 60, 180, 360, 360, 360;
1, 13, 78, 234, 468, 468, 468, 468;
1, 14, 84, 336, 672, 1344, 1344, 1344;
1, 15, 105, 420, 1260, 2520, 2520, 2520, 2520;
1, 16, 112, 448, 1344, 2688, 2688, 2688, 2688; ...
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MATHEMATICA
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t[n_, k_] := Product[Floor[n/j - 1], {j, 1, k}]; Flatten[Table[t[n, k], {n, 0, 15}, {k, 0, Floor[n/2]}]] (* Jean-François Alcover, Jun 12 2012 *)
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PROG
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(PARI) {T(n, k)=if(k==0, 1, prod(j=1, k, floor(n/j-1)))}
for(n=0, 12, for(k=0, n\2, print1(T(n, k), ", ")); print(""))
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CROSSREFS
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KEYWORD
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nonn,nice,tabf
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AUTHOR
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STATUS
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approved
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