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Search: id:A098361
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| A098361 |
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Multiplication table of the factorial numbers read by antidiagonals. |
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+0
4
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| 1, 1, 1, 2, 1, 2, 6, 2, 2, 6, 24, 6, 4, 6, 24, 120, 24, 12, 12, 24, 120, 720, 120, 48, 36, 48, 120, 720, 5040, 720, 240, 144, 144, 240, 720, 5040, 40320, 5040, 1440, 720, 576, 720, 1440, 5040, 40320, 362880, 40320, 10080, 4320, 2880, 2880, 4320, 10080, 40320
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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This sequence gives the variance of the 2-dimensional Polynomial Chaoses (See the Stochastic Finite Elements reference) - Stephen Crowley (crow(AT)crowlogic.net), Mar 28 2007
Row sums are A003149. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
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REFERENCES
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R. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach (Revised Edition), 2003, Ch 2.4 Table 2-2.
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FORMULA
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t(n,m)=(n+1)!*Beta[n-m+1,m+1]. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
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EXAMPLE
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The antidiagonals are {1}, {1, 1}, {2, 1, 2}, {6, 2, 2, 6}, {24, 6, 4, 6, 24}, {120, 24, 12, 12, 24, 120}, {720, 120, 48, 36, 48, 120, 720}, {5040, 720, 240, 144, 144, 240, 720, 5040}, {40320, 5040, 1440, 720, 576, 720, 1440, 5040, 40320}, {362880, 40320, 10080, 4320, 2880, 2880, 4320, 10080, 40320, 362880}, {3628800, 362880, 80640, 30240, 17280, 14400, 17280, 30240, 80640, 362880, 3628800} [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
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MATHEMATICA
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Table[Table[(n + 1)!*Beta[n - m + 1, m + 1], {m, 0, n}], {n, 0, 10}] Flatten[%] (*A003149*) Table[Sum[(n + 1)!*Beta[n - m + 1, m + 1], {m, 0, n}], {n, 0, 10}] [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
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CROSSREFS
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Cf. A003991, A098358, A098359, A098360.
Cf. A003149 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
Sequence in context: A133644 A152431 A143965 this_sequence A050977 A053448 A060550
Adjacent sequences: A098358 A098359 A098360 this_sequence A098362 A098363 A098364
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KEYWORD
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nonn,tabl
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004
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