%I #16 Oct 01 2016 09:08:20
%S 1,5,13,31,58,106,170,270,395,575,791,1085,1428,1876,2388,3036,3765,
%T 4665,5665,6875,8206,9790,11518,13546,15743,18291,21035,24185,27560,
%U 31400,35496,40120,45033,50541,56373,62871,69730,77330,85330,94150
%N Second elementary symmetric function of the first n terms of (1,1,2,2,3,3,4,4,...).
%C Second subdiagonal of A246117. - _Peter Bala_, Aug 15 2014
%F Conjectural o.g.f.: x^2*(1 + 3*x + x^2 + x^3)/((1 - x^2)^3*(1 - x)^2). - _Peter Bala_, Aug 15 2014
%F Conjectural closed form: 64*a(n) = 2*n^2 -16*n/3 -3 +16*n^3/3 +2*n^4 +(-1)^n *(3-2*n^2). - _R. J. Mathar_, Oct 01 2016
%t f[k_] := Floor[(k + 1)/2]; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[2, t[n]]
%t Table[a[n], {n, 2, 50}] (* A203246 *)
%Y Cf. A203298, A203299, A246117, A212523 (bisection ?), A103220 (bisection?)
%K nonn
%O 2,2
%A _Clark Kimberling_, Dec 31 2011