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A110770
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Triangle read by rows: T(n,k) = binomial(t(n) - t(k-1),k), where t(j) = j*(j+1)/2; 1<=k<=n.
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2
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1, 3, 1, 6, 10, 1, 10, 36, 35, 1, 15, 91, 220, 126, 1, 21, 190, 816, 1365, 462, 1, 28, 351, 2300, 7315, 8568, 1716, 1, 36, 595, 5456, 27405, 65780, 54264, 6435, 1, 45, 946, 11480, 82251, 324632, 593775, 346104, 24310, 1, 55, 1431, 22100, 211876, 1221759
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
1;
3, 1;
6, 10, 1;
10, 36, 35, 1;
15, 91, 220, 126, 1;
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MAPLE
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t:=n->n*(n+1)/2: T:=proc(n, k) if k<=n then binomial(t(n)-t(k-1), k) else 0 fi end: for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form. - Emeric Deutsch, Oct 09 2006
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MATHEMATICA
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Table[Binomial[Binomial[n + 1, 2] - Binomial[k, 2], k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Oct 19 2017 *)
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PROG
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(PARI) for(n=1, 10, for(k=1, n, print1(binomial(binomial(n+1, 2) - binomial(k, 2), k), ", "))) \\ G. C. Greubel, Oct 19 2017
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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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