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A157108
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Triangle, read by rows, T(n, k) = binomial(n*binomial(n, k), k).
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1
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1, 1, 1, 1, 4, 1, 1, 9, 36, 1, 1, 16, 276, 560, 1, 1, 25, 1225, 19600, 12650, 1, 1, 36, 4005, 280840, 2555190, 376992, 1, 1, 49, 10731, 2421090, 146475945, 534017484, 13983816, 1, 1, 64, 24976, 14885696, 4053946260, 147055790784, 163995687856, 621216192, 1
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text;
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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, 6, 47, 854, 33502, 3217065, 696909117, 315741551830, 339451781249846, 856885032450030756, ...}.
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LINKS
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FORMULA
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T(n, k) = binomial(n*binomial(n, k), k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 4, 1;
1, 9, 36, 1;
1, 16, 276, 560, 1;
1, 25, 1225, 19600, 12650, 1;
1, 36, 4005, 280840, 2555190, 376992, 1;
1, 49, 10731, 2421090, 146475945, 534017484, 13983816, 1;
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MAPLE
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seq(seq( binomial(n*binomial(n, k), 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, k], k], {n, 0, 10}, {k, 0, n}]//Flatten
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PROG
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(PARI) T(n, k) = binomial(n*binomial(n, k), k); \\ G. C. Greubel, Nov 30 2019
(Magma) [Binomial(n*Binomial(n, k), k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 30 2019
(Sage) [[binomial(n*binomial(n, k), 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, k), 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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