[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,2
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: A377811 A179494 A295255 * A304340 A336227 A119820
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 29 2011
STATUS
approved