A171731 revision #3
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A171731
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Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).
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0
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0, 1, 0, 1, 2, 0, 2, 3, 3, 0, 3, 8, 6, 4, 0, 5, 15, 20, 10, 5, 0, 8, 30, 45, 40, 15, 6, 0, 13, 56, 105, 105, 70, 21, 7, 0, 21, 104, 224, 280, 210, 112, 28, 8, 0, 34, 189, 468, 672, 630, 378, 168, 36, 9, 0, 55, 340, 945, 1560, 1680, 1260, 630, 240, 45, 10, 0
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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Sum_{k, 0<=k<=n} T(n,k)*x^k = A000045(n), A001906(n), A093131(n), A099453(n-1), A081574(n), A081575(n) for x = 0,1,2,3,4,5 respectively. Sum_{k, 0<=k<=n} T(n,k)*2^(n-k) = A014445(n).
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EXAMPLE
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Triangle begins : 0 ; 1,0 ; 1,2,0 ; 2,3,3,0 ; 3,8,6,4,0 ; 5,15,20,10,5,0 ; ...
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MATHEMATICA
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Flatten[Table[Binomial[n, k]Fibonacci[n-k], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jan 16 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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editing
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