A203006 (n-1)-st elementary symmetric function of the first n Fibonacci numbers.

1, 2, 5, 17, 91, 758, 10094, 215094, 7378716, 408057060, 36439600740, 5258207000160, 1226732478115680, 462844011818878560, 282472779283129656000, 278884771717353348456000, 445462025196173918554440000, 1151206495594319717393795136000

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 the integers F(j), j=1..n, form a triangle T(n,k), 0<=k<=n, n>=0:

1;

1, 1;

1, 2, 1;

1, 4, 5, 2;

1, 7, 17, 17, 6;

which is the unsigned version of A158472. This here is the first subdiagonal. The diagonal seems to be A003266. The 2nd column is A000071, the 3rd A190173, the 4th A213787. (End)

Examples

			0th elementary symmetric function: 1
1st e.s.f. of {1,1}: 1+1=2
2nd e.s.f. of {1,1,2}: 1*1+1*2+2*2=5
		

Links

• Robert Israel, Table of n, a(n) for n = 1..98

Crossrefs

Cf. A000045.

Programs

Maple

f:= proc(n) local x,P,i;
P:= mul(x+combinat:-fibonacci(i),i=1..n);
coeff(P,x,1)
end proc:
map(f, [$1..20]); # Robert Israel, Aug 18 2024

Mathematica

f[k_] := Fibonacci[k]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 18}]  (* A203006 *)