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

%I

%S 1,4,39,1080,88209,21493836,15683355351,34309958505840,

%T 225130514549271201,4431394012508602048404,

%U 261672339357326993189906439,46354644349343413982791427120040,24634789450813795903041020740742981169

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

%F a(n) = (1/2)*(3-1/3^(n-1))*3^(binomial(n,2)). - _Emanuele Munarini_, Sep 14 2017

%t f[k_] := 3^(k - 1); t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 16}] (* A203197 *)

%t Table[1/2 (3 - 1/3^(n-1)) 3^Binomial[n, 2], {n, 1, 20}] (* _Emanuele Munarini_, Sep 14 2017 *)

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

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 30 2011

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)