cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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