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Search: id:A142473
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| A142473 |
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A division triangle sequence of the Stirling numbers of the first kind by the binomial ( Pascal's triangle): t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m]. |
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+0
1
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| 1, -1, 2, 4, -6, 6, -36, 44, -36, 24, 576, -600, 420, -240, 120, -14400, 13152, -8100, 4080, -1800, 720, 518400, -423360, 233856, -105840, 42000, -15120, 5040, -25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320, 1625702400, -1104606720, 510295680, -193777920, 64653120
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 1, 4, -4, 276, -6348, 254976, -13188096, 887086080, -74869297920}.
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REFERENCES
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t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m].
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FORMULA
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t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m].
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EXAMPLE
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{1},
{-1, 2},
{4, -6, 6},
{-36, 44, -36, 24},
{576, -600, 420, -240, 120},
{-14400, 13152, -8100, 4080, -1800, 720},
{518400, -423360, 233856, -105840, 42000, -15120, 5040},
{-25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320},
{1625702400, -1104606720, 510295680, -193777920, 64653120, -19595520, 5503680, -1451520, 362880},
{-131681894400, 82783088640, -35462448000, 12505190400, -3878280000, 1093357440, -285768000, 70156800, -16329600, 3628800}
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MATHEMATICA
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t[n_, m_] = n!*StirlingS1[n, m]/Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A087459 A123258 A104968 this_sequence A132426 A072646 A162672
Adjacent sequences: A142470 A142471 A142472 this_sequence A142474 A142475 A142476
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 21 2008
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