Recursive function in bash

There are several syntax and a quite obvious logic one (return 0)

A working version is below:

#!/bin/bash

factorial()
{
    if (( $1 <= 1 )); then
        echo 1
    else
        last=$(factorial $(( $1 - 1 )))
        echo $(( $1 * last ))
    fi
}
factorial 5

You are missing:

1. return is bad (should use echo)

2. shbang line (is /bin/bash not /bash/bin)

3. Can't do arithmetic outside of (( )) or $(( )) (or let, but (( )) is preferred)

echo-ing a result may be the only way to get a result for n > 5, but capturing the echo'ed result requires a subshell, which means the recursion will get expensive fast. A cheaper solution is to use a variable:

factorial() {
    local -i val=${val:-($1)}
    if (( $1 <= 1 )); then
        echo $val
        return
    fi
    (( val *= $1 - 1 ))
    factorial $(( $1 - 1 ))
}

If you want to be extra sure that val is unset when you start, use a wrapping function:

factorial() {
    local -i val=$1
    _fact() {
        if (( $1 <= 1 )); then
            echo $val
            return
        fi
        (( val *= $1 - 1 ))
        _fact $(( $1 - 1 ))
    }
    _fact $1
}

For comparison:

# My Method
$ time for i in {0..100}; do factorial $(( RANDOM % 21 )); done > /dev/null 

real    0m0.028s
user    0m0.026s
sys     0m0.001s

# A capturing-expression solution
$ time for i in {0..100}; do factorial $(( RANDOM % 21 )); done > /dev/null 

real    0m0.652s
user    0m0.221s
sys     0m0.400s

#!/bin/bash

function factorial() 
{ 
   if (( $1 < 2 ))
   then
     echo 1
   else
     echo $(( $1 * $(factorial $(( $1 - 1 ))) ))
   fi
}

This will work better.

(It works up to 25, anyway, which should be enough to prove the point about recursion.)

For higher numbers, bc would be the tool to use, making the ninth line above:

echo "$1 * $(factorial $(( $1 - 1 )))" | bc

but you have to be a bit careful with bc --

$ factorial 260
38301958608361692351174979856044918752795567523090969601913008174806\
51475135399533485285838275429773913773383359294010103333339344249624\
06009974551133984962615380298039823284896547262282019684886083204957\
95233137023276627601257325925519566220247124751398891221069403193240\
41688318583612166708334763727216738353107304842707002261430265483385\
20637683911007815690066342722080690052836580858013635214371395680329\
58941156051513954932674117091883540235576934400000000000000000000000\
00000000000000000000000000000000000000000

was quite a strain on my poor system!