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

%I #7 Oct 01 2016 11:55:22

%S 1,3,11,61,518,6974,149574,5151036,285534660,25535107140,

%T 3687959921760,860864908848480,324911938205144160,

%U 198334214378751672000,195840008156732278248000,312839537789862069432264000

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

%C From _R. J. Mathar_, Oct 01 2016 (Start):

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

%C 1

%C 1 1

%C 1 3 2

%C 1 6 11 6

%C 1 11 41 61 30

%C 1 19 129 389 518 240

%C 1 32 376 2066 5575 6974 3120

%C 1 53 1048 9962 48961 124049 149574 65520

%C 1 87 2850 45594 387669 1788723 4367240 5151036 2227680

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

%t f[k_] := Fibonacci[k + 1]; t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 16}] (* A203007 *)

%Y Cf. A000045, A203006.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 29 2011

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)