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A142243
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A doubling of A062344 that gives a skew triangle of coefficients: t(n,m)=(Binomial[2*n, m]*Binomial[2*(n - m), (n - m)]).
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0
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1, 2, 2, 6, 8, 6, 20, 36, 30, 20, 70, 160, 168, 112, 70, 252, 700, 900, 720, 420, 252, 924, 3024, 4620, 4400, 2970, 1584, 924, 3432, 12936, 22932, 25480, 20020, 12012, 6006, 3432, 12870, 54912, 110880, 141120, 127400, 87360, 48048, 22880, 12870, 48620
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are:
{2, 14, 86, 510, 2992, 17522, 102818, 605470, 3579980, 21254064}.
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FORMULA
| t(n,m)=(Binomial[2*n, m]*Binomial[2*(n - m), (n - m)]).
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EXAMPLE
| {1},
{2, 2},
{6, 8, 6},
{20, 36, 30, 20},
{70, 160, 168, 112, 70},
{252, 700, 900, 720, 420, 252},
{924, 3024, 4620, 4400, 2970, 1584, 924},
{3432, 12936, 22932, 25480, 20020, 12012, 6006, 3432},
{12870, 54912, 110880, 141120, 127400, 87360, 48048, 22880, 12870},
{48620, 231660, 525096, 753984, 771120, 599760, 371280, 190944, 87516, 48620},
{184756, 972400, 2445300, 3912480, 4476780, 3907008, 2713200, 1550400, 755820, 335920, 184756}
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MATHEMATICA
| t[n_, m_] = (Binomial[2*n, m]*Binomial[2*(n - m), (n - m)]); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A062344.
Sequence in context: A134457 A092522 A116542 * A091441 A099490 A167878
Adjacent sequences: A142240 A142241 A142242 * A142244 A142245 A142246
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 17 2008
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