A203007 (n-1)-st elementary symmetric function of Fibonacci numbers F(2) to F(n).

1, 3, 11, 61, 518, 6974, 149574, 5151036, 285534660, 25535107140, 3687959921760, 860864908848480, 324911938205144160, 198334214378751672000, 195840008156732278248000, 312839537789862069432264000

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Comments

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

The k-th elementary symmetric functions of F(j), j=2..n+1, form a triangle T(n,k), 0<=k<=n, n>=0:

1

1 1

1 3 2

1 6 11 6

1 11 41 61 30

1 19 129 389 518 240

1 32 376 2066 5575 6974 3120

1 53 1048 9962 48961 124049 149574 65520

1 87 2850 45594 387669 1788723 4367240 5151036 2227680

This here is the first subdiagonal. The diagonal is A003266. The 2nd column is A001911, the 3rd A203245. (End)

Crossrefs

Cf. A000045, A203006.

Programs

Mathematica

f[k_] := Fibonacci[k + 1]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A203007 *)