A203148 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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 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

FORMULA

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

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 *)

PROG

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

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