The stupid question is the question not asked PerlMonks

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```0: #!perl -w
1:
2: # BinomialExpansion.pl
3:
4: # usage perl BinomialExpansion.pl n, where n is an integer > 0
5:
6: # ** the memory goes crazy after the 170th power
7: # the expansion of (x+y)^170 peaks at 9.14484184513157e+049 * x^85 * y^85
8: # so you can imagine what happens if you put int n>170
9:
10: my \$n = (\$_=shift) > 0 ? int \$_ :
11:         die "'usage perl BinomialExpansion.pl 9, where n > 0'";
12:
13: print _titled_hr(' Binomial Expansion For (x+y)^',\$n,' ');
14:
15: for my \$j (0 .. \$n)
16: {
17:     my \$coefficient = nCr(\$n,\$j);
18:     my \$nj=\$n-\$j;
19:     print \$coefficient;
20:     print \$_ = (\$nj!=0)?( (\$nj>1)?(' * x^'.\$nj):(' * x') ):'';
21:     print \$_ = (\$j!=0)?( (\$j==1)?(' * y'):(' * y^'.\$j) ):'';
22:     print \$_ = (\$j!=\$n)?(" +\n"):("\n");
23: }
24:
25: print ' 'x 25,' = (x + y)^',\$n, "\n"x 3;
26:
27: # returns n!/r!(n-r)!
28: sub nCr
29: {
30:     my \$n=shift;
31:     my \$r=shift;
32:
33:     return int nFactorial(\$n) / int nFactorial(\$r) * int nFactorial(\$n-\$r);
34: }
35:
36: # like the name says, n!
37: sub nFactorial
38: {
39:     my \$n=shift;
40:     my \$product = 1;
41:
42:     while(\$n>0)
43:     {
44:         \$product *= \$n--;
45:     }
46:
47:     return  \$product;
48: }
49:
50: # neat little titled hr, that does a < 80 chars since int rounds down
51: # i really, really, like it
52: sub _titled_hr
53: {
54:     my \$string = join('', @_);
55:     my \$oy = int (80 -(length \$string) )/ 2;
56:     return "\n","-" x \$oy, \$string, "-" x \$oy,"\n";
57: }
58:
59: __END__
60: # some random things i say
61: #1
62: "--. .-. . . - --..   -.-- .----. .- .-.. .-.."
63:
64: #2
65: "...- .-. --- --- -- --..--   ...- .-. --- --- -- .----."
66:
67: #3
68: --- ..-.   .- .-.. .-..   - .... .   - .... .. -. --. ...   ..   .-.. --- ... -
69: --..--
70:   ..   -- .. ... ...   -- -.--   -- .. -. -..   - .... .   -- --- ... - .-.-.-
71:     -....- -....-   --- --.. --.. .. .   --- ... -... --- ..- .-. -. .
72:
73: # a lil sample from my machine
74:
75: F:\>perl BinomialExpansion.pl 9
76: 1 * x^9 +
77: 9 * x^8 * y +
78: 36 * x^7 * y^2 +
79: 84 * x^6 * y^3 +
80: 126 * x^5 * y^4 +
81: 126 * x^4 * y^5 +
82: 84 * x^3 * y^6 +
83: 36 * x^2 * y^7 +
84: 9 * x * y^8 +
85: 1 *  * y^9
86:                  = (x + y)^9
87: F:\>
88:
89: # Notice a pattern? Fleet attack!
90: # >
91: #   >
92: #     >
93: #     >
94: #       >
95: #       >
96: #     >
97: #     >
98: #   >
99: # >```

In reply to Binomial Expansion by crazyinsomniac

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