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A203165 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,4,1,2,3,4,1,2,...).

%I A203165 #8 Jul 02 2013 11:14:09
%S A203165 1,7,19,50,174,768,1056,2400,7776,32832,39744,86400,273024,1133568,
%T A203165 1299456,2764800,8626176,35500032,39481344,82944000,256794624,
%U A203165 1051066368,1146617856,2388787200,7357464576,30003167232,32296402944,66886041600
%N A203165 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,4,1,2,3,4,1,2,...).
%F A203165 Conjecture: G.f. x*(1+7*x+19*x^2+50*x^3+126*x^4+432*x^5+144*x^6) / (-1+24*x^4)^2 with a(n) = 48*a(n-4)-576*a(n-8). - _R. J. Mathar_, Jul 02 2013
%t A203165 f[k_] := 1 + Mod[k + 1, 4];
%t A203165 t[n_] := Table[f[k], {k, 1, n}]
%t A203165 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203165 Table[a[n], {n, 1, 33}]  (* A203165 *)
%Y A203165 Cf. A010883, A203162, A203163, A203164.
%K A203165 nonn
%O A203165 1,2
%A A203165 _Clark Kimberling_, Dec 30 2011