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A203159
(n-1)-st elementary symmetric function of {2,4,6,8,...,2n}.
1
1, 6, 44, 400, 4384, 56448, 836352, 14026752, 262803456, 5441863680, 123436892160, 3044235018240, 81112101027840, 2322150583173120, 71092846618214400, 2317820965473484800, 80177108784198451200, 2932996578806543155200
OFFSET
1,2
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
EXAMPLE
(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
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 *)
CROSSREFS
Cf. A004041.
Sequence in context: A286867 A361649 A084965 * A279085 A124996 A226045
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 29 2011
STATUS
approved