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A203007
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(n-1)-st elementary symmetric function of Fibonacci numbers F(2) to F(n).
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1
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1, 3, 11, 61, 518, 6974, 149574, 5151036, 285534660, 25535107140, 3687959921760, 860864908848480, 324911938205144160, 198334214378751672000, 195840008156732278248000, 312839537789862069432264000
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OFFSET
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1,2
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COMMENTS
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The k-th elementary symmetric functions of F(j), j=2..n+1, form a triangle T(n,k), 0<=k<=n, n>=0:
1
1 1
1 3 2
1 6 11 6
1 11 41 61 30
1 19 129 389 518 240
1 32 376 2066 5575 6974 3120
1 53 1048 9962 48961 124049 149574 65520
1 87 2850 45594 387669 1788723 4367240 5151036 2227680
This here is the first subdiagonal. The diagonal is A003266. The 2nd column is A001911, the 3rd A203245. (End)
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LINKS
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MATHEMATICA
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f[k_] := Fibonacci[k + 1]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A203007 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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