A203197 (n-1)-st elementary symmetric function of the first n terms of (1,3,9,27,...)=A000244.

1, 4, 39, 1080, 88209, 21493836, 15683355351, 34309958505840, 225130514549271201, 4431394012508602048404, 261672339357326993189906439, 46354644349343413982791427120040, 24634789450813795903041020740742981169

Offset: 1

Author

Clark Kimberling, Dec 30 2011

Keywords

• nonn

Crossrefs

Cf. A000244, A003462 (1st symm. func.), A203243 (2nd symm. func.).

Programs

Mathematica

f[k_] := 3^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}]  (* A203197 *)
Table[1/2 (3 - 1/3^(n-1)) 3^Binomial[n, 2], {n, 1, 20}] (* Emanuele Munarini, Sep 14 2017 *)

Formula

a(n) = (1/2)*(3-1/3^(n-1))*3^(binomial(n,2)). - Emanuele Munarini, Sep 14 2017