%I #11 Oct 01 2016 10:14:18
%S 4,16,37,77,133,223,338,506,710,990,1319,1751,2247,2877,3588,4468,
%T 5448,6636,7945,9505,11209,13211,15382,17902,20618,23738,27083,30891,
%U 34955,39545,44424,49896,55692,62152,68973,76533,84493,93271,102490
%N Second elementary symmetric function of the first n terms of (2,2,3,3,4,4,5,5...).
%F Empirical g.f.: -x^2*(x+2)*(x^4-x^3-3*x^2+3*x+2) / ((x-1)^5*(x+1)^3). - _Colin Barker_, Aug 15 2014
%F Empirical: a(n) = n^3/3 +25*n^2/32 -23*n/24 -11/64 +n^4/32 +(-1)^n* (-n^2/32 -n/8 +11/64). - _R. J. Mathar_, Oct 01 2016
%t f[k_] := Floor[(k + 3)/2]; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[2, t[n]]
%t Table[a[n], {n, 2, 50}] (* A203299 *)
%Y Cf. A203246, A203298.
%K nonn
%O 2,1
%A _Clark Kimberling_, Dec 31 2011