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A137259
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Triangle T(n, k) = n*( (n-1)! - (k-1)! ), read by rows.
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1
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0, 0, 0, 3, 3, 0, 20, 20, 16, 0, 115, 115, 110, 90, 0, 714, 714, 708, 684, 576, 0, 5033, 5033, 5026, 4998, 4872, 4200, 0, 40312, 40312, 40304, 40272, 40128, 39360, 34560, 0, 362871, 362871, 362862, 362826, 362664, 361800, 356400, 317520, 0, 3628790, 3628790, 3628780, 3628740, 3628560, 3627600, 3621600, 3578400, 3225600, 0
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OFFSET
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1,4
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LINKS
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Krassimir Penev, The Fubini Principle, The American Mathematical Monthly, Vol. 115, No. 3 (Mar., 2008), pp. 245-248.
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FORMULA
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T(n, k) = n! - n*(k-1)!.
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EXAMPLE
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Triangle begins as:
0;
0, 0;
3, 3, 0;
20, 20, 16, 0;
115, 115, 110, 90, 0;
714, 714, 708, 684, 576, 0;
5033, 5033, 5026, 4998, 4872, 4200, 0;
40312, 40312, 40304, 40272, 40128, 39360, 34560, 0;
362871, 362871, 362862, 362826, 362664, 361800, 356400, 317520, 0;
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MAPLE
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MATHEMATICA
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T[n_, k_]:= n! - n*(k-1)!;
Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 10 2021 *)
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PROG
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(Magma) [n*(Factorial(n-1) - Factorial(k-1)): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2021
(Sage) flatten([[n*(factorial(n-1) - factorial(k-1)) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 10 2021
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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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