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

1,2

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)

Links

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

Example

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

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 *)

Crossrefs

Cf. A000045.

Sequence in context: A195137 A026822 A059248 * A143878 A081546 A103511

Adjacent sequences: A203003 A203004 A203005 * A203007 A203008 A203009

Keyword

nonn

Author

Clark Kimberling, Dec 29 2011

Status

approved