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A209330
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Triangle defined by T(n,k) = binomial(n^2, n*k), for n>=0, k=0..n, as read by rows.
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10
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1, 1, 1, 1, 6, 1, 1, 84, 84, 1, 1, 1820, 12870, 1820, 1, 1, 53130, 3268760, 3268760, 53130, 1, 1, 1947792, 1251677700, 9075135300, 1251677700, 1947792, 1, 1, 85900584, 675248872536, 39049918716424, 39049918716424, 675248872536, 85900584, 1, 1
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OFFSET
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0,5
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COMMENTS
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Ignoring initial row T(0,0), equals the logarithmic derivative of the g.f. of triangle A209196.
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LINKS
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EXAMPLE
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The triangle of coefficients C(n^2,n*k), n>=k, k=0..n, begins:
1;
1, 1;
1, 6, 1;
1, 84, 84, 1;
1, 1820, 12870, 1820, 1;
1, 53130, 3268760, 3268760, 53130, 1;
1, 1947792, 1251677700, 9075135300, 1251677700, 1947792, 1;
1, 85900584, 675248872536, 39049918716424, 39049918716424, 675248872536, 85900584, 1; ...
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MATHEMATICA
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Table[Binomial[n^2, n*k], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 05 2018 *)
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PROG
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(PARI) {T(n, k)=binomial(n^2, n*k)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
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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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