Project Euler # 76: ways can one hundred be written as a sum

It is possible to write five as a sum in exactly six different ways:

4 + 1
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1

How many different ways can one hundred be written as a sum of at least two positive integers?


int n = 100;
int[][] a = new int[n + 1][n + 1];
int i, j, k;
for (i = 0; i < a.length; i++) {
a[i][0] = 0;
a[0][i] = 1;
}
for (i = 1; i < a.length; i++) {
a[i][1] = 1;
for (j = 2; j < a[0].length; j++) {
k = i - j;
if (k < 0)
a[i][j] = a[i][j - 1];
else
a[i][j] = a[i][j - 1] + a[k][j];
}
}
i--;
int answer = a[i][i - 1];

BIG FACTORIAL!!!!!!! Java Code :)

public static void main(String[] args) throws IOException {
long start = System.currentTimeMillis();

int[] answerArray = new int[10000];
answerArray[0] = 1;

int maxAnswerDigit = 1;
int FACTORIAL_OF = 1000;
for (int n = 1; n <= FACTORIAL_OF; n++) {
for (int digit = 0; digit < maxAnswerDigit; digit++)
answerArray[digit] = answerArray[digit] * n;

for (int digit = 0; digit < maxAnswerDigit; digit++) {
if (answerArray[digit] > 9) {
answerArray[digit + 1] += answerArray[digit] / 10;
answerArray[digit] = answerArray[digit] % 10;
if (digit + 1 == maxAnswerDigit)
maxAnswerDigit++;

}
}
}
for (int i = maxAnswerDigit - 1; i >= 0; i--) {
System.out.print(answerArray[i]);
sum += answerArray[i];
}
System.out.println("\nSum=" + sum);

System.out.println("answered in "
+ (System.currentTimeMillis() - start) / 1000.0 + " sec.");

}

=================
Bloody hell 1000! =
402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Sum of its digit =10539
answered in 0.062 sec