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• Syntax error: use no quotes inside arithmetic evaluation.
• Logic error: you are mixing STDOUT and return values.

Either pass values as STDOUT:

function factorial { (( $1 )) && echo $(( $1 * $( factorial $(( $1 - 1 )) ) )) || echo 1 } factorial 5 

Or return them:

function factorial { (( $1 )) || return 1 factorial $(( $1 - 1 )) return $(( $1 * $? )) } factorial 5 echo $? 

Both codes work in bash, ksh (93 sure, no idea about 88) and zsh, so I guess yes, shells do support recursion.