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Search: id:A123743
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| A123743 |
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Certain Vandermonde determinants with Fibonacci numbers. |
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1
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| 1, 2, 12, 1440, 7257600, 4981616640000, 1190690865178214400000, 272795714695463271824306995200000, 157357907118293002525216789633250308915200000000
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OFFSET
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1,2
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COMMENT
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The determinant of a Vandermonde matrix VM_n with elements VM_n[i,j]=(x_j)^i, i,j,=1..n, is VdmII([x_1,...,x_n]) := Det(VM_n)= product(x_k,k=1,...,n)*product(x_j - x_i, 1<=i<j<=n) if n>=2. For n=1, Det(VM_1)=1.
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FORMULA
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a(n)= Fibfac(n)* |A123742(n)|, with the Fibonacci factorials Fibfac(n):=A003266(n+1).
a(n)=VdmII([F(2),F(3),...,F(n+1)]) := Det(VM_n[i,j]) with the Vandermonde matrix elements VM_n[i,j]:=F(j+1)^i, i,j,=1..n, and F(k):=A000045(k) (Fibonacci).
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EXAMPLE
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n=4: VM_4 = matrix([1,2,3,5],[1,4,9,25],[1,8,27,125],[1,16,81,625]).
a(4)=Det(VM_4) = 1440 = 30*48 = A003266(5)*|A123742(4)|.
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CROSSREFS
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Cf. A123742 (another version).
Sequence in context: A022482 A081701 A069714 this_sequence A111180 A085912 A085895
Adjacent sequences: A123740 A123741 A123742 this_sequence A123744 A123745 A123746
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 13 2006
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