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 A203157 (n-1)-st elementary symmetric function of the first n triangular numbers. 1
 1, 4, 27, 288, 4500, 97200, 2778300, 101606400, 4629441600, 257191200000, 17116074360000, 1344389840640000, 123067686661920000, 12988374315396480000, 1565562975516540000000, 213751531590524928000000, 32817539834507780352000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA Conjecture: 2*(-n+1)*a(n) +n^3*a(n-1)=0. - R. J. Mathar, Oct 01 2016 EXAMPLE 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 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 *) CROSSREFS Cf. A000217, A006472 (n-th symm. func.), A000292 (1st symm. func.). Sequence in context: A193467 A179494 A295255 * A304340 A119820 A159599 Adjacent sequences:  A203154 A203155 A203156 * A203158 A203159 A203160 KEYWORD nonn AUTHOR Clark Kimberling, Dec 29 2011 STATUS approved

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Last modified June 19 13:26 EDT 2019. Contains 324222 sequences. (Running on oeis4.)