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A203299 Second elementary symmetric function of the first n terms of (2,2,3,3,4,4,5,5...). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..40.

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

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 *)

CROSSREFS

Cf. A203246, A203298.

Sequence in context: A080709 A256322 A080855 * A198015 A103770 A121318

Adjacent sequences:  A203296 A203297 A203298 * A203300 A203301 A203302

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 31 2011

STATUS

approved

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Last modified November 15 08:58 EST 2019. Contains 329144 sequences. (Running on oeis4.)