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A203166 (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,5,1,2,3,4,5,...)=A010884.

%I A203166 #8 Jul 02 2013 11:14:30
%S A203166 1,3,11,50,274,394,908,2964,12576,65760,80160,174720,552960,2298240,
%T A203166 11836800,13564800,28857600,90028800,370483200,1893888000,2101248000,
%U A203166 4409856000,13644288000,55821312000,284083200000,308966400000
%N A203166 (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,5,1,2,3,4,5,...)=A010884.
%F A203166 Conjecture: G.f. x*(1+3*x+11*x^2+50*x^3+274*x^4+154*x^5+188*x^6+324*x^7+576*x^8) / (-1+120*x^5)^2  with a(n) = 240*a(n-5) -14400*a(n-10). - _R. J. Mathar_, Jul 02 2013
%t A203166 f[k_] := 1 + Mod[k + 4, 5];
%t A203166 t[n_] := Table[f[k], {k, 1, n}]
%t A203166 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203166 Table[a[n], {n, 1, 33}]  (* A203166 *)
%Y A203166 Cf. A010884, A203163.
%K A203166 nonn
%O A203166 1,2
%A A203166 _Clark Kimberling_, Dec 30 2011