A203148 (n-1)-st elementary symmetric function of {3,9,...,3^n}.

1, 12, 351, 29160, 7144929, 5223002148, 11433166050879, 75035879252272080, 1477081305957768349761, 87223128348206814118735932, 15451489966710801620870785316511, 8211586182553137756809552940033725880, 13091937140529934508508023103481190655434529

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Comments

From R. J. Mathar, Oct 01 2016: (Start)

The k-th elementary symmetric functions of the integers 3^j, j=1..n, form a triangle T(n,k), 0<=k<=n, n>=0:

1;

1 3;

1 12 27;

1 39 351 729;

1 120 3510 29160 59049;

1 363 32670 882090 7144929 14348907;

which is the row-reversed version of A173007. This here is the first subdiagonal. The diagonal seems to be A047656. The first column is A029858. (End)

Links

• G. C. Greubel, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A203149.

Cf. A029858, A047656, A173007.

Programs

Magma

[(1/2)*(3^n -1)*3^(Binomial(n,2)): n in [1..20]]; // G. C. Greubel, Feb 24 2021

Mathematica

f[k_]:= 3^k; t[n_]:= Table[f[k], {k, 1, n}];
a[n_]:= SymmetricPolynomial[n - 1, t[n]];
Table[a[n], {n, 1, 16}] (* A203148 *)
Table[1/2 (3^n - 1) 3^Binomial[n, 2], {n, 1, 20}] (* Emanuele Munarini, Sep 14 2017 *)

Sage

[(1/2)*(3^n -1)*3^(binomial(n,2)) for n in (1..20)] # G. C. Greubel, Feb 24 2021

Formula

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