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A109906
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A triangle of coefficients based on A000045 and the Pascal's triangle: t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].
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0
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1, 1, 1, 2, 2, 2, 3, 6, 6, 3, 5, 12, 24, 12, 5, 8, 25, 60, 60, 25, 8, 13, 48, 150, 180, 150, 48, 13, 21, 91, 336, 525, 525, 336, 91, 21, 34, 168, 728, 1344, 1750, 1344, 728, 168, 34, 55, 306, 1512, 3276, 5040, 5040, 3276, 1512, 306, 55, 89, 550, 3060, 7560, 13650, 16128
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums are:
{1, 2, 6, 18, 58, 186, 602, 1946, 6298, 20378, 65946}
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FORMULA
| t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].
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EXAMPLE
| {1},
{1, 1},
{2, 2, 2},
{3, 6, 6, 3},
{5, 12, 24, 12, 5},
{8, 25, 60, 60, 25, 8},
{13, 48, 150, 180, 150, 48, 13},
{21, 91, 336, 525, 525, 336, 91, 21},
{34, 168, 728, 1344, 1750, 1344, 728, 168, 34},
{55, 306, 1512, 3276, 5040, 5040, 3276, 1512, 306, 55},
{89, 550, 3060, 7560, 13650, 16128, 13650, 7560, 3060, 550, 89}
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MATHEMATICA
| Clear[t, n, m] t[n_, m_] := Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A141611, A141617, A000045.
Sequence in context: A156820 A104346 A193450 * A104856 A038715 A057040
Adjacent sequences: A109903 A109904 A109905 * A109907 A109908 A109909
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Aug 24 2008
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