A203159 (n-1)-st elementary symmetric function of {2,4,6,8,...,2n}.

1, 6, 44, 400, 4384, 56448, 836352, 14026752, 262803456, 5441863680, 123436892160, 3044235018240, 81112101027840, 2322150583173120, 71092846618214400, 2317820965473484800, 80177108784198451200, 2932996578806543155200

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Examples

			(n-1)-st elementary symmetric function of {2,4,6,8,...,2n}.
Let esf abbreviate "elementary symmetric function".  Then
0th esf of {2}:  1
1st esf of {2,4}: 2+4=6
2nd esf of {2,4,6}: 2*4+2*6+4*6=44
		

Crossrefs

Cf. A004041.

Programs

Mathematica

f[k_] := 2 k; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A203159 *)

Formula

Conjecture: a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)^2*a(n-2)=0. - R. J. Mathar, Oct 01 2016