1 1 -> 2

 2 3 -> 28,27

 3 1 -> 4,19

 3 4,5 -> 381,70

 1 9.379 -> 18.758

 0 48 -> 1

÷2µØP*÷!
ç×*@

÷2µØP*÷! - Link 1: n, r
÷2       - n / 2
  µ      - monadic chain separation
   ØP    - π (3.141592653589793)
     *   - exponentiate: π^(n/2)
       ! - Pi(n/2): Gamma(n/2 + 1)
      ÷  - divide: π^(n/2) / Gamma(n/2 + 1)

ç×*@     - Main link: n, r
ç        - call last link (1) as a dyad: π^(n/2) / Gamma(n/2 + 1)
  *@     - exponentiate with reversed @rguments: r^n
 ×       - multiply: r^n * π^(n/2) / Gamma(n/2 + 1)

Pi^(a=.5#)/a!#2^#&

N[Pi^(#/2)/Gamma[#/2 + 1] #2^#] &
Pi^(.5#)/Gamma[.5# + 1] #2^# &    (* replace exact with approximate numbers*)
Pi^(.5#)/(.5#)! #2^# &            (* n! == Gamma[n + 1] *)
Pi^(a=.5#)/a! #2^# &              (* replace repeated .5# *)
Pi^(a=.5#)/a!#2^#&                (* remove whitespace *)

function(n,r)pi^(n/2)/gamma(n/2+1)*r^n

function(n,r)c(1,pi,4/3*pi)[n]*r^n

0%r=1
1%r=2*r
n%r=2*pi*r^2/n*(n-2)%r

n%r=(max 1$1-(-1)**n)*(2*pi)^(floor$n/2)*r**n/product[n,n-2..1.1]

d=(n,r)=>r**n*(n<2?n+1:Math.PI*(n<3?1:4/3))

3:^[2P4*P/3]*1hi)

3:         % Push array [1 2 3]
           % STACK: [1 2 3]
^          % Take r implicitly, and raise it to [1 2 3] element-wise
           % STACK: [3 9 27]
[2P4*P/3]  % Push array [2 pi 4*pi/3]
           % STACK: [3 9 27], [2 pi 4*pi/3]
*          % Multiply element-wise
           % STACK: [6 28.2743 113.0973]
1h         % Append 1
           % STACK: [6 28.2743 113.0973, 1]
i)         % Input n and use it as modular index into the array. Display implicitly
           % STACK: 28.2743

v 0 r=1
v 1 r=2*r
v n r=2*pi*r*r*v(n-2)r/n

let v 0 r=1
    v 1 r=2*r
    v n r=2*pi*r*r*(v(n-2)r)/n

(define(v d r)(match d[0 1][1(* 2 r)][_(/(* 2 pi r r(v(- d 2)r))d)]))

(define(v d r)
  (match d
    [0 1]
    [1 (* 2 r)]
    [_ (/ (*  2   pi   r   r   (v (- d 2) r)  )
          d)]
    ))

(v 1 1)
(v 2 3)
(v 3 1)
(v 3 4.5)
(v 1 9.379)
(v 0 48)

2
28.274333882308138
4.1887902047863905
381.7035074111599
18.758
1

@a=1..2;push@a,6.283/$_*@a[$_-2]for 2..($b=<>);say$a[$b]*<>**$b

{import math._;(n,r)=>pow(r,n)*Seq(1,2,Pi,Pi*4/3)(n)}

{                     //define a block, the type of this is the type of the last expression, which is a function
  import math._;        //import everything from math, for pow and pi
  (n,r)=>               //define a function
    pow(r,n)*             //r to the nth power multiplied by
    Seq(1,2,Pi,Pi*4/3)(n) //the nth element of a sequence of 1, 2, Pi and Pi*4/3
}

(n,r)=>[1,r+r,a=Math.PI*r*r,a*r*4/3][n]

from math import*
f=lambda n,r:n*r*2*(n<2or pi*r/n/n*(f(n-2,r)or 1))

from math import*
f=lambda n,r:1*(n<1)or r*2*(n<2)or 2*pi*r*r/n*f(n-2,r)

from math import*
lambda n,r:pi**(n/2)*r**n/gamma(n/2+1)

#N,R::((if (< N 2) ((? (!= 0 N) (* 2 R) 1)) ((/ (* (* (* (* (f (- N 2) R) 2)
        3.1416) R) R) N))))

% n-circle.lithp
(
    (def f #N,R::((if (< N 2) ((? (!= 0 N) (* 2 R) 1)) ((/ (* (* (* (* (f (- N 2) R) 2) 3.1416) R) R) N)))))
    (print (f 1 1))
    (print (f 2 3))
    (print (f 3 1))
    (print (f 3 4.5))
    (print (f 1 9.379))
    (print (f 0 48))
)

#./run.js n-circle.lithp
2
28.274333882308138
4.1887902047863905
381.7035074111598
18.758
1

{1$_[2dP]*<f*,:)-2%./1+:*}

{            e# Begin block: stack holds d r
  1$_[2dP]*< e#   Build a list which repeats [2 pi] d times and take the first d elements
  f*         e#   Multiply each element of the list by r
  ,:)-2%    e#   Build a list [1 ... d] and take every other element starting at the end
  ./         e#   Pointwise divide. The d/2 elements of the longer list are untouched
  1+:*       e#   Add 1 to ensure the list is non-empty and multiply its elements
}