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A360208
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Triangular array T(n,k) read by antidiagonals T(n,k) = F(n)!/(F(k)!*F(n-k)!), where F(m) = A000045(m) = m-th Fibonacci number.
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2
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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 6, 3, 1, 1, 20, 60, 60, 20, 1, 1, 336, 6720, 10080, 6720, 336, 1, 1, 154440, 51891840, 518918400, 518918400, 51891840, 154440, 1, 1, 8204716800, 1267136462592000, 212878925715456000, 1419192838103040000, 212878925715456000, 1267136462592000, 8204716800, 1
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OFFSET
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0,8
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COMMENTS
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Analogous to Pascal's triangle, A007318.
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LINKS
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FORMULA
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T(n,k) = F(n)!/(F(k)!*F(n - k)!), where F(m) = A000045(m) = m-th Fibonacci number.
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EXAMPLE
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First seven rows:
1
1 1
1 1 1
1 2 2 1
1 3 6 3 1
1 20 60 60 20 1
1 336 6720 10080 6720 336 1
...
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MAPLE
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F:= combinat[fibonacci]:
T:= (n, k)-> F(n)!/(F(k)!*F(n-k)!):
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MATHEMATICA
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f[n_] := Fibonacci[n];
t = Table[f[n]!/(f[k]!*f[n - k]!), {n, 0, 8}, {k, 0, n}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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