

A203006


(n1)st elementary symmetric function of the first n Fibonacci numbers.


2



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

1,2


COMMENTS

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

Table of n, a(n) for n=1..18.


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


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



