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A094310
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Triangle read by rows: T(n,k), the k-th term of the n-th row, is the product of all numbers from 1 to n except k: T(n,k) = n!/k.
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4
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1, 2, 1, 6, 3, 2, 24, 12, 8, 6, 120, 60, 40, 30, 24, 720, 360, 240, 180, 144, 120, 5040, 2520, 1680, 1260, 1008, 840, 720, 40320, 20160, 13440, 10080, 8064, 6720, 5760, 5040, 362880, 181440, 120960, 90720, 72576, 60480, 51840, 45360, 40320, 3628800
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The sum of the rows gives A000254 (Stirling numbers of first kind). The first column and the leading diagonal are factorials given by A000142 with offsets of 0 and 1.
T(n,k) is the number of length k cycles in all permutations of {1,2,...,n}.
T(n,k)*k = n*n! = A001563(n).
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FORMULA
| E.g.f. for column k is x^k/k/(1-x).
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EXAMPLE
| 1,
2, 1,
6, 3, 2,
24, 12, 8, 6,
120, 60, 40, 30, 24,
720, 360, 240, 180, 144, 120,
5040, 2520, 1680, 1260, 1008, 840, 720,
40320, 20160, 13440, 10080, 8064, 6720, 5760, 5040
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MATHEMATICA
| Table[Table[n!/k, {k, 1, n}], {n, 1, 10}]
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CROSSREFS
| Cf. A061579, A094307.
Cf. A129825. - Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 18 2009
C.f. A001710, A002301, A133799.
Sequence in context: A125901 A094307 A097905 * A165908 A121281 A131449
Adjacent sequences: A094307 A094308 A094309 * A094311 A094312 A094313
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KEYWORD
| nonn,tabl
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 29 2004
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EXTENSIONS
| More terms from Philippe DELEHAM, Jun 11 2005
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