print "non-recursive version"
print catNonRec(5)
for i = 0 to 15
    print i;"   =   "; catNonRec(i)
next
print

print "recursive version"
print catRec(5)
for i = 0 to 15
    print i;"   =   "; catRec(i)
next
print

print "recursive with memoisation"
redim cats(20)  'clear the array
print catRecMemo(5)
for i = 0 to 15
    print i;"   =   "; catRecMemo(i)
next
print


wait

function catNonRec(n)   'non-recursive version
    catNonRec=1
    for i=1 to n
        catNonRec=((2*((2*i)-1))/(i+1))*catNonRec
    next
end function

function catRec(n)  'recursive version
    if n=0 then
        catRec=1
    else
        catRec=((2*((2*n)-1))/(n+1))*catRec(n-1)
    end if
end function

function catRecMemo(n)  'recursive version with memoisation
    if n=0 then
        catRecMemo=1
    else
        if cats(n-1)=0 then    'call it recursively only if not already calculated
            prev = catRecMemo(n-1)
        else
            prev = cats(n-1)
        end if
        catRecMemo=((2*((2*n)-1))/(n+1))*prev
    end if
    cats(n) = catRecMemo    'memoisation for future use
end function