login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203154 (n-1)-st elementary symmetric function of {2, 3, 3, 4, 4, 5, 5,...,Floor[(n+4)/2]}. 3
1, 5, 21, 102, 480, 2688, 14880, 96480, 622080, 4613760, 34110720, 285586560, 2386298880, 22289541120, 207921530880, 2145056256000, 22108972032000, 249782787072000, 2820035699712000, 34637103857664000, 425205351825408000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
EXAMPLE
Let esf abbreviate "elementary symmetric function". Then
0th esf of {2}: 1
1st esf of {2,3}: 2+3=5;
2nd esf of {2,3,3} is 2*3+2*3+3*3=21.
MAPLE
SymmPolyn := proc(L::list, n::integer)
local c, a, sel;
a :=0 ;
sel := combinat[choose](nops(L), n) ;
for c in sel do
a := a+mul(L[e], e=c) ;
end do:
a;
end proc:
A203154 := proc(n)
[seq(floor((k+4)/2), k=1..n)] ;
SymmPolyn(%, n-1);
end proc: # R. J. Mathar, Sep 23 2016
# second Maple program:
f:= proc(n) local L, x;
if n::odd then L:= `*`(x+2, seq((x+i)$2, i=3..2+n/2))
else L:= `*`(seq((x+i)*(x+i+1), i=2..1+n/2))
fi;
coeff(L, x, 1);
end proc:
map(f, [$1..50]); # Robert Israel, Nov 27 2017
MATHEMATICA
f[k_] := Floor[(k + 4)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203154 *)
CROSSREFS
Sequence in context: A362556 A046633 A280623 * A097175 A100284 A337168
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 29 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 10:31 EDT 2024. Contains 373516 sequences. (Running on oeis4.)