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

1,2

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;

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

Crossrefs

Cf. A203149.

Cf. A029858, A047656, A173007.

Sequence in context: A209425 A171206 A219407 * A120813 A202926 A134800

Adjacent sequences: A203145 A203146 A203147 * A203149 A203150 A203151

Keyword

nonn

Author

Clark Kimberling, Dec 29 2011

Status

approved