A203157 (n-1)-st elementary symmetric function of the first n triangular numbers.

1, 4, 27, 288, 4500, 97200, 2778300, 101606400, 4629441600, 257191200000, 17116074360000, 1344389840640000, 123067686661920000, 12988374315396480000, 1565562975516540000000, 213751531590524928000000, 32817539834507780352000000

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Examples

			Let esf abbreviate "elementary symmetric function".  Then
0th esf of {1}:  1
1st esf of {1,3}:  1+3=4
2nd esf of {1,3,6} is 1*3+1*6+3*6=27
		

Crossrefs

Cf. A000217, A006472 (n-th symm. func.), A000292 (1st symm. func.).

Programs

Mathematica

f[k_] := k (k + 1)/2; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}]  (* A203157 *)

Formula

Conjecture: 2*(-n+1)*a(n) +n^3*a(n-1)=0. - R. J. Mathar, Oct 01 2016