A203299 Second elementary symmetric function of the first n terms of (2,2,3,3,4,4,5,5...).

4, 16, 37, 77, 133, 223, 338, 506, 710, 990, 1319, 1751, 2247, 2877, 3588, 4468, 5448, 6636, 7945, 9505, 11209, 13211, 15382, 17902, 20618, 23738, 27083, 30891, 34955, 39545, 44424, 49896, 55692, 62152, 68973, 76533, 84493, 93271, 102490

Offset: 2

Author

Clark Kimberling, Dec 31 2011

Keywords

• nonn

Crossrefs

Cf. A203246, A203298.

Programs

Mathematica

f[k_] := Floor[(k + 3)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 50}]  (* A203299 *)

Formula

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

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