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A093447
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Triangle a(n,k) read by rows n which contain columns k=1,2,..,n, where each entry is the product of numbers (k-1)*n-T(k-2)+1 through k*n-T(k-1).
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2
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1, 2, 3, 6, 20, 6, 24, 210, 72, 10, 120, 3024, 1320, 182, 15, 720, 55440, 32760, 4896, 380, 21, 5040, 1235520, 1028160, 175560, 13800, 702, 28, 40320, 32432400, 39070080, 7893600, 657720, 32736, 1190, 36, 362880, 980179200, 1744364160
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is built by starting from the sequence 1,2,....,T(n) in row n, where T(n) is the triangular number A000217(n) and packaging its first n, the next n-1, the next n-2,... up to the last number in groups and writing down the product of each group in one cell of the triangle. The first column is A000142. The second column is essentially A006963. The 3rd column is essentially A001763. The diagonal is A000217. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 26 2007
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FORMULA
| a(n,k)= [k*n-T(k-1)]!/[(k-1)*n-T(k-2)]! where T(n)=A000217(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 26 2007
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EXAMPLE
| In factorized notation the triangle starts
1;
1*2, 3;
1*2*3, 4*5, 6;
1*2*3*4, 5*6*7, 8*9, 10;
1*2*3*4*5, 6*7*8*9, 10*11*12, 13*14, 15;
which gives
1;
2, 3;
6, 20, 6;
24, 210, 72, 10;
120, 3024, 1320, 182, 15;
720,55440,32760, 4896, 380, 21;
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MAPLE
| A000217 := proc(n) n*(n+1)/2 ; end: A093447 := proc(n, k) factorial(k*n-A000217(k-1))/factorial((k-1)*n-A000217(k-2)) ; end: for n from 1 to 16 do for k from 1 to n do printf("%d, ", A093447(n, k)) ; od ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 26 2007
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CROSSREFS
| Cf. A093445, A093446, A093448.
Sequence in context: A075633 A141048 A124066 * A173744 A176806 A168268
Adjacent sequences: A093444 A093445 A093446 * A093448 A093449 A093450
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KEYWORD
| nonn,tabl
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 02 2004
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 26 2007
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