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

1,2

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)

Links

Table of n, a(n) for n=1..23.

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

Cf. A203152, A246117.

Sequence in context: A051436 A378004 A054581 * A140440 A005664 A364761

Adjacent sequences: A203148 A203149 A203150 * A203152 A203153 A203154

Keyword

nonn

Author

Clark Kimberling, Dec 29 2011

Status

approved