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A203006
(n-1)-st elementary symmetric function of the first n Fibonacci numbers.
3
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 29 2011
STATUS
approved