|
|
A203151
|
|
(n-1)-st elementary symmetric function of {1,1,2,2,3,3,4,4,5,5,...,Floor[(n+1)/2]}.
|
|
2
|
|
|
1, 2, 5, 12, 40, 132, 564, 2400, 12576, 65760, 408960, 2540160, 18299520, 131725440, 1079205120, 8836853760, 81157386240, 745047797760, 7582159872000, 77138417664000, 861690783744000, 9623448705024000, 117074735382528000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The k-th elementary symmetric functions of the repeated integers 1,1,2,2,..[(n+1)/2], form a triangle T(n,k), 0<=k<=n, n>=0:
1
1 1
1 2 1
1 4 5 2
1 6 13 12 4
1 9 31 51 40 12
which is a row-reversed version of A246117. This here is the first subdiagonal. The diagonal is A010551. The 2nd column is A002620, the 3rd A203246. (End)
|
|
LINKS
|
|
|
EXAMPLE
|
Let esf abbreviate "elementary symmetric function". Then
0th esf of {2}: 1;
1st esf of {1,1}: 1+1=2;
2nd esf of {1,1,2} is 1*1+1*2+1*2=5.
|
|
MATHEMATICA
|
f[k_] := Floor[(k + 1)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203151 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|