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A157219
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A binomial tent triangle sequence: tent function: f(n,m)=If[k <= Floor[n/2], k, n - k]; t(n,m)=Binomial[n*f[n, m], f[n, m]].
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 28, 4, 1, 1, 5, 45, 45, 5, 1, 1, 6, 66, 816, 66, 6, 1, 1, 7, 91, 1330, 1330, 91, 7, 1, 1, 8, 120, 2024, 35960, 2024, 120, 8, 1, 1, 9, 153, 2925, 58905, 58905, 2925, 153, 9, 1, 1, 10, 190, 4060, 91390, 2118760, 91390, 4060, 190, 10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 4, 8, 38, 102, 962, 2858, 40266, 123986, 2310062,...}.
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FORMULA
| Tent function: f(n,m)=If[k <= Floor[n/2], k, n - k]; t(n,m)=Binomial[n*f[n, m], f[n, m]].
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EXAMPLE
| {1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 28, 4, 1},
{1, 5, 45, 45, 5, 1},
{1, 6, 66, 816, 66, 6, 1},
{1, 7, 91, 1330, 1330, 91, 7, 1},
{1, 8, 120, 2024, 35960, 2024, 120, 8, 1},
{1, 9, 153, 2925, 58905, 58905, 2925, 153, 9, 1},
{1, 10, 190, 4060, 91390, 2118760, 91390, 4060, 190, 10, 1}
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MATHEMATICA
| Clear[t, n, m]; f[n_, k_] := If[k <= Floor[n/2], k, n - k];
t[n_, m_] = Binomial[n*f[n, m], f[n, m]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A159623 A143199 A137896 * A167040 A054450 A174802
Adjacent sequences: A157216 A157217 A157218 * A157220 A157221 A157222
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 25 2009
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