%I #11 Nov 28 2017 11:35:51
%S 1,6,44,400,4384,56448,836352,14026752,262803456,5441863680,
%T 123436892160,3044235018240,81112101027840,2322150583173120,
%U 71092846618214400,2317820965473484800,80177108784198451200,2932996578806543155200
%N (n-1)-st elementary symmetric function of {2,4,6,8,...,2n}.
%F Conjecture: a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Oct 01 2016
%e (n-1)-st elementary symmetric function of {2,4,6,8,...,2n}.
%e Let esf abbreviate "elementary symmetric function". Then
%e 0th esf of {2}: 1
%e 1st esf of {2,4}: 2+4=6
%e 2nd esf of {2,4,6}: 2*4+2*6+4*6=44
%t f[k_] := 2 k; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 16}] (* A203159 *)
%Y Cf. A004041.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 29 2011
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