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A157109
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Triangle, read by rows, T(n, k) = binomial(n*binomial(n, floor((n-k)/2)), k).
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1
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1, 1, 1, 1, 2, 1, 1, 9, 3, 1, 1, 16, 120, 4, 1, 1, 50, 300, 2300, 5, 1, 1, 90, 4005, 7140, 58905, 6, 1, 1, 245, 10731, 518665, 211876, 1906884, 7, 1, 1, 448, 100128, 1848224, 102114376, 7624512, 74974368, 8, 1, 1, 1134, 285390, 71728020, 450710001, 28845440064, 324540216, 3477216600, 9, 1
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OFFSET
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0,5
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COMMENTS
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Row sums are: {1, 2, 4, 14, 142, 2657, 70148, 2648410, 186662066, 33169921436, 11592123179902, ...}.
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LINKS
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FORMULA
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T(n, k) = binomial(n*binomial(n, floor((n-k)/2)), k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 9, 3, 1;
1, 16, 120, 4, 1;
1, 50, 300, 2300, 5, 1;
1, 90, 4005, 7140, 58905, 6, 1;
1, 245, 10731, 518665, 211876, 1906884, 7, 1;
1, 448, 100128, 1848224, 102114376, 7624512, 74974368, 8, 1;
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MAPLE
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seq(seq( binomial(n*binomial(n, floor((n-k)/2)), k), k=0..n), n=0..10); # G. C. Greubel, Nov 30 2019
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MATHEMATICA
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Table[Binomial[n*Binomial[n, Floor[(n-m)/2]], m], {n, 0, 10}, {k, 0, n}]//Flatten
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PROG
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(PARI) T(n, k) = binomial(n*binomial(n, (n-k)\2), k); \\ G. C. Greubel, Nov 30 2019
(Magma) [Binomial(n*Binomial(n, Floor((n-k)/2)), k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 30 2019
(Sage) [[binomial(n*binomial(n, floor((n-k)/2)), k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 30 2019
(GAP) Flat(List([0..10], n-> List([0..n], k-> Binomial(n*Binomial(n, Int((n-k)/2)), k) ))); # G. C. Greubel, Nov 30 2019
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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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