Edit Simplified. Correct bug of 0 missing
Defined as a function, then counting 10 more byte for output using alert()
Important Really this one is not valid according to the rules, because javascript can not handle big numbers. For instance with parameters 2,5 it can't find 2^2^2^2^2 (ie 2^65536). A number this big is 'Infinity' in javascript.
Edit Simplified. Correct bug of 0 missing
To be golfed. I have an idea I want to share: use a postfix notation. In postfix any type of expression is made just of values and operators - no parentheses needed. The postfix notation can be translated to usual algebraic infix notation - but that's out of scope in this challenge.
F=(n, k, g={})=>{ k += k - 1; // Count in base 6 - '0' means Value, '1'..'5' means operators // A valid expression starts with Value twice, then n operators intermixed with n-1 Values // x: Coded expression, l: Expression length, k Expression maxlimit length from param for (l = i = 1; x = i.toString(6), l += !!x[l], l<k; i++) if (x.split(0).length*2 == l+1) // check balancing values/operators { for (s = [n,n], p = l; o = x[--p];) // Calc stack starts with N,N if (-o) // If not '0' b=s.pop(),a=s.pop(), // Do calc s.push(o<2 ? a+b : o<3 ? a-b : o<4 ? a*b : o<5 ? a/b : Math.pow(a,b)) else // Push value s.push(n) // r = Math.floor(s.pop()); // Last result in stack r >= 0 & isFinite(r) & !isNaN(r) & !g[r] && (g[r]=x) // Put in hashtable avoiding duplicates } // Uncomment this to see the postfix expression list // for (i in g) console.log(i, [n,n,...[...g[i]].reverse().map(v=>v>0?'x+-*/^'[v]:n)]) return Object.keys(g) // Retust list of hashtable keys }