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A288778
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Triangle read by rows (1<=k<=n): T(n,k) = (n-k+1)*k! - (k-1)!
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2
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0, 1, 1, 2, 3, 4, 3, 5, 10, 18, 4, 7, 16, 42, 96, 5, 9, 22, 66, 216, 600, 6, 11, 28, 90, 336, 1320, 4320, 7, 13, 34, 114, 456, 2040, 9360, 35280, 8, 15, 40, 138, 576, 2760, 14400, 75600, 322560, 9, 17, 46, 162, 696, 3480, 19440, 115920, 685440, 3265920, 10, 19, 52, 186, 816, 4200, 24480, 156240, 1048320, 6894720, 36288000
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OFFSET
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1,4
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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 begins:
0;
1, 1;
2, 3, 4;
3, 5, 10, 18;
4, 7, 16, 42, 96;
5, 9, 22, 66, 216, 600;
6, 11, 28, 90, 336, 1320, 4320;
7, 13, 34, 114, 456, 2040, 9360, 35280;
8, 15, 40, 138, 576, 2760, 14400, 75600, 322560;
9, 17, 46, 162, 696, 3480, 19440, 115920, 685440, 3265920;
10, 19, 52, 186, 816, 4200, 24480, 156240, 1048320, 6894720, 36288000;
...
For n = 10 and k = 2; T(10,2) = 17 coincides with the number of positive terms with two digits in A215014 (see the first comment above).
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MATHEMATICA
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Table[(n - k + 1) k! - (k - 1)!, {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Jun 16 2017 *)
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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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