|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|