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Task/Catalan-numbers/Nim/catalan-numbers.nim

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+import strutils
+
+proc binomial(m, n): auto =
+  result = 1
+  var
+    d = m - n
+    n = n
+    m = m
+  if d > n:
+    n = d
+
+  while m > n:
+    result *= m
+    dec m
+    while d > 1 and (result mod d) == 0:
+      result = result div d
+      dec d
+
+proc catalan1(n): auto =
+  binomial(2 * n, n) div (n + 1)
+
+proc catalan2(n): auto =
+  if n == 0:
+    result = 1
+  for i in 0 .. <n:
+    result += catalan2(i) * catalan2(n - 1 - i)
+
+proc catalan3(n): int =
+  if n > 0: 2 * (2 * n - 1) * catalan3(n - 1) div (1 + n)
+  else: 1
+
+for i in 0..15:
+  echo align($i, 7), " ", align($catalan1(i), 7), " ", align($catalan2(i), 7), " ", align($catalan3(i), 7)