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%I #13 Oct 01 2016 11:00:23
%S 1,2,5,17,91,758,10094,215094,7378716,408057060,36439600740,
%T 5258207000160,1226732478115680,462844011818878560,
%U 282472779283129656000,278884771717353348456000,445462025196173918554440000,1151206495594319717393795136000
%N (n-1)-st elementary symmetric function of the first n Fibonacci numbers.
%C From _R. J. Mathar_, Oct 01 2016: (Start)
%C The k-th elementary symmetric functions of the integers F(j), j=1..n, form a triangle T(n,k), 0<=k<=n, n>=0:
%C 1;
%C 1, 1;
%C 1, 2, 1;
%C 1, 4, 5, 2;
%C 1, 7, 17, 17, 6;
%C which is the unsigned version of A158472. This here is the first subdiagonal. The diagonal seems to be A003266. The 2nd column is A000071, the 3rd A190173, the 4th A213787. (End)
%e 0th elementary symmetric function: 1
%e 1st e.s.f. of {1,1}: 1+1=2
%e 2nd e.s.f. of {1,1,2}: 1*1+1*2+2*2=5
%t f[k_] := Fibonacci[k]; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 18}] (* A203006 *)
%Y Cf. A000045.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 29 2011
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