c# - Calculating Catalan Number -

i using code calculate catalan number. gives me right value until n=6 , gives me wrong values. checked manually using calculator. ex: when n=5 catalan number 42 right when n=7 , gives me 6 wrong answer should 429. cant figure out whats wrong. can 1 me please?

static void main(string[] args) {     int i, n, fact, fact1, fact2, catalann;     console.writeline("enter number (n>=0)");      n = convert.toint32(console.readline());     fact = n;      (i = n - 1; > 0; i--)     {         fact = fact * i;     }     console.writeline("" + fact);     console.readline();      fact1 = 2*n;      (i = 2*n - 1; > 0; i--)     {         fact1 = fact1 * i;     }     console.writeline("" + fact1);     console.readline();      fact2 = n+1;      (i = (n+1)-1; > 0; i--)     {         fact2 = fact2 * i;     }     console.writeline("" + fact2);     console.readline();      catalann = fact1 / (fact2 * fact);     console.writeline("catalan number of given number : " + catalann);     console.readline(); } 

if change second loop to:

for (i = 2*n - 1; > 0; i--) {     int old = fact1;     fact1 = fact1 * i;     console.writeline("" + old + " " + fact1); } 

then you'll see you're suffering overflow (slightly reformatted line values):

        14        182        182       2184       2184      24024      24024     240240     240240    2162160    2162160   17297280   17297280  121080960  121080960  726485760  726485760 -662538496 <- overflow occurs here. -662538496 1644813312 1644813312  639472640  639472640 1278945280 1278945280 1278945280 

this due factorial-type terms in calculations. changing type long give more breathing space (allowing c₁₀). beyond that, decimal can go little further may have end using arbitrary-precision math library (like system.numerics.biginteger) higher numbers.

you may want use less onerous calculation minimises interim terms little:

n = convert.toint32(console.readline()); catalann = 1; term = 0; while (n-- > 1) {     term++;     catalann = catalann * (4 * term + 2) / (term + 2); } 

this give more breathing space, regardless of data type use. our lowly int can c₁₆ calculation, long can @ least c₂₅, far bothered check.