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%I #12 Oct 01 2016 12:06:25
%S 1,4,27,288,4500,97200,2778300,101606400,4629441600,257191200000,
%T 17116074360000,1344389840640000,123067686661920000,
%U 12988374315396480000,1565562975516540000000,213751531590524928000000,32817539834507780352000000
%N (n-1)-st elementary symmetric function of the first n triangular numbers.
%F Conjecture: 2*(-n+1)*a(n) +n^3*a(n-1)=0. - _R. J. Mathar_, Oct 01 2016
%e Let esf abbreviate "elementary symmetric function". Then
%e 0th esf of {1}: 1
%e 1st esf of {1,3}: 1+3=4
%e 2nd esf of {1,3,6} is 1*3+1*6+3*6=27
%t f[k_] := k (k + 1)/2; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 22}] (* A203157 *)
%Y Cf. A000217, A006472 (n-th symm. func.), A000292 (1st symm. func.).
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 29 2011
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