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A098361
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Multiplication table of the factorial numbers read by antidiagonals.
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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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
Antidiagonal sums are A003149. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
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REFERENCES
| 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
| T(n,k) = n!*k! = (k+n)!/binomial(k+n,n). [From Peter Luschny (peter(AT)luschny.de), Aug 23 2010, corrected R. J. Mathar, Dec 10 2010]
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EXAMPLE
| The array starts in row n=0 with columns k>=0 as:
.......1........1........2........6.......24......120.
.......1........1........2........6.......24......120.
.......2........2........4.......12.......48......240.
.......6........6.......12.......36......144......720.
......24.......24.......48......144......576.....2880.
.....120......120......240......720.....2880....14400.
.....720......720.....1440.....4320....17280....86400.
....5040.....5040....10080....30240...120960...604800.
...40320....40320....80640...241920...967680..4838400.
..362880...362880...725760..2177280..8709120.43545600.
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MAPLE
| seq(print(seq(k!*(n-k)!, k=0..n)), n=0..6); [From Peter Luschny (peter(AT)luschny.de), Aug 23 2010]
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MATHEMATICA
| 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
| Cf. A003991, A098358, A098359, A098360.
Cf. A003149 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2008]
Sequence in context: A133644 A152431 A143965 * A050977 A053448 A060550
Adjacent sequences: A098358 A098359 A098360 * A098362 A098363 A098364
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KEYWORD
| nonn,tabl
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AUTHOR
| Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004
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