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A141902
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A triangle sequence of coefficients based on A000984: t(n,m)=(2*n)!/((n - m)!*m!)^2.
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1
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1, 2, 2, 6, 24, 6, 20, 180, 180, 20, 70, 1120, 2520, 1120, 70, 252, 6300, 25200, 25200, 6300, 252, 924, 33264, 207900, 369600, 207900, 33264, 924, 3432, 168168, 1513512, 4204200, 4204200, 1513512, 168168, 3432, 12870, 823680, 10090080, 40360320
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are:
{1, 4, 36, 400, 4900, 63504, 853776, 11778624, 165636900, 2363904400, 34134779536}.
Based on reduction of the multinomial:
t(n,m,k,l)=(n+k)1/((n-m)1*m!*(k-l)!*l!)
by symmetry.
The first column is A000984.
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FORMULA
| t(n,m)=(2*n)!/((n - m)!*m!)^2.
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EXAMPLE
| {1},
{2, 2},
{6, 24, 6},
{20, 180, 180, 20},
{70, 1120, 2520, 1120, 70},
{252, 6300, 25200, 25200, 6300, 252},
{924, 33264, 207900, 369600, 207900, 33264, 924},
{3432, 168168, 1513512, 4204200, 4204200, 1513512, 168168, 3432},
{12870, 823680, 10090080, 40360320, 63063000, 40360320, 10090080, 823680, 12870},
{48620, 3938220, 63011520, 343062720, 771891120, 771891120, 343062720, 63011520, 3938220, 48620},
{184756, 18475600, 374130900, 2660486400, 8147739600, 11732745024, 8147739600, 2660486400, 374130900,18475600, 184756}
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MATHEMATICA
| Clear[t, n, m, k, l]; t[n_, m_] = (2*n)!/((n - m)!*m!)^2; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A000984.
Sequence in context: A138801 A188958 A069466 * A143084 A188962 A076741
Adjacent sequences: A141899 A141900 A141901 * A141903 A141904 A141905
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 13 2008
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