A203151 (n-1)-st elementary symmetric function of {1,1,2,2,3,3,4,4,5,5,...,Floor[(n+1)/2]}.

1, 2, 5, 12, 40, 132, 564, 2400, 12576, 65760, 408960, 2540160, 18299520, 131725440, 1079205120, 8836853760, 81157386240, 745047797760, 7582159872000, 77138417664000, 861690783744000, 9623448705024000, 117074735382528000

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Comments

Column 3 of A246117. - Peter Bala, Aug 15 2014

From R. J. Mathar, Oct 01 2016 (Start):

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)

Examples

			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.
		

Crossrefs

Cf. A203152, A246117.

Programs

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 *)