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A203009 (n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(0)=2.

%I A203009 #8 Oct 01 2016 11:10:28
%S A203009 1,3,11,50,374,4282,78924,2322060,110101476,8413051008,1038251025216,
%T A203009 207035781419520,66749863269991104,34803836775900988992,
%U A203009 29353783726459293724224,40050488883338399323186560,88407698594458813846355350656
%N A203009 (n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(0)=2.
%C A203009 From _R. J. Mathar_, Oct 01 2016 (Start):
%C A203009 The k-th elementary symmetric functions of the A000032(j), j=0..n-1, form a triangle T(n,k), 0<=k<=n, n>=0:
%C A203009 1
%C A203009 1 2
%C A203009 1 3 2
%C A203009 1 6 11 6
%C A203009 1 10 35 50 24
%C A203009 1 17 105 295 374 168
%C A203009 1 28 292 1450 3619 4282 1848
%C A203009 1 46 796 6706 29719 69424 78924 33264
%C A203009 1 75 2130 29790 224193 931275 2092220 2322060 964656
%C A203009 This here is the first subdiagonal. The diagonal is A135407. The 2nd column is A001610, the 3rd A242300, the 4th A213807. (End)
%t A203009 f[k_] := LucasL[k - 1]; t[n_] := Table[f[k], {k, 1, n}]
%t A203009 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203009 Table[a[n], {n, 1, 16}] (* A203009 *)
%Y A203009 Cf. A203010.
%K A203009 nonn
%O A203009 1,2
%A A203009 _Clark Kimberling_, Dec 29 2011