Catalan numbers: Difference between revisions

BigInt factorial(in uint n) {

alias mfact = memoize!factorial mfact;

return n ? mfact(n - 1) * n : BigInt(1).BigInt;

auto cats1(in uint n) {

return factorial(2 * n) / (factorial(n + 1) * factorial(n).factorial);

BigInt cats2(in uint n) {

alias mcats2 = memoize!cats2 mcats2;

if (n == 0) return BigInt(1).BigInt;

autoBigInt sum = BigInt(0);

foreach (immutable i; 0 .. n)

BigInt cats3(in uint n) {

alias mcats3 = memoize!cats3 mcats3;

return n ? (4*n - 2) * mcats3(n - 1) / (n + 1) : BigInt(1).BigInt;

foreach (immutable i; 0 .. 15)

writefln("%2d => %s %s %s", i, cats1(i).cats1, cats2(i).cats2, cats3(i).cats3);