|
%I #31 Feb 25 2021 08:32:16
%S 1,12,351,29160,7144929,5223002148,11433166050879,75035879252272080,
%T 1477081305957768349761,87223128348206814118735932,
%U 15451489966710801620870785316511,8211586182553137756809552940033725880,13091937140529934508508023103481190655434529
%N (n-1)-st elementary symmetric function of {3,9,...,3^n}.
%C From _R. J. Mathar_, Oct 01 2016: (Start)
%C 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:
%C 1;
%C 1 3;
%C 1 12 27;
%C 1 39 351 729;
%C 1 120 3510 29160 59049;
%C 1 363 32670 882090 7144929 14348907;
%C 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)
%H G. C. Greubel, <a href="/A203148/b203148.txt">Table of n, a(n) for n = 1..60</a>
%F a(n) = (1/2)*(3^n-1)*3^(binomial(n,2)). - _Emanuele Munarini_, Sep 14 2017
%t f[k_]:= 3^k; t[n_]:= Table[f[k], {k, 1, n}];
%t a[n_]:= SymmetricPolynomial[n - 1, t[n]];
%t Table[a[n], {n, 1, 16}] (* A203148 *)
%t Table[1/2 (3^n - 1) 3^Binomial[n, 2], {n, 1, 20}] (* _Emanuele Munarini_, Sep 14 2017 *)
%o (Sage) [(1/2)*(3^n -1)*3^(binomial(n,2)) for n in (1..20)] # _G. C. Greubel_, Feb 24 2021
%o (Magma) [(1/2)*(3^n -1)*3^(Binomial(n,2)): n in [1..20]]; // _G. C. Greubel_, Feb 24 2021
%Y Cf. A203149.
%Y Cf. A029858, A047656, A173007.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 29 2011
| 