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Task/Catalan-numbers/EchoLisp/catalan-numbers.echolisp

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+(lib 'sequences)
+(lib 'bigint)
+(lib 'math)
+
+;; function definition
+(define (C1 n) (/ (factorial (* n 2)) (factorial (1+ n)) (factorial n)))
+(for ((i [1 .. 16])) (write (C1 i)))
+    → 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845
+
+;; using a recursive procedure with memoization
+(define (C2 n) ;; ( Σ  ...)is the same as (sigma ..)
+	(Σ (lambda(i) (* (C2 i) (C2 (- n i 1))))  0 (1- n)))
+(remember 'C2 #(1)) ;; first term defined here
+
+(for ((i [1 .. 16])) (write (C2 i)))
+    → 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845
+
+
+;; using procrastinators = infinite sequence
+(define (catalan n acc) (/ (* acc 2 (1- (* 2 n))) (1+ n)))
+(define C3 (scanl catalan 1 [1 ..]))
+(take C3 15)
+    → (1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845)
+
+
+;; the same, using infix notation
+(lib 'match)
+(load 'infix.glisp)
+
+(define (catalan n acc) ((2 * acc * ( 2 * n - 1)) / (n + 1)))
+(define C3 (scanl catalan 1 [1 ..]))
+
+(take C3 15)
+    → (1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845)
+;; or
+(for ((c C3) (i 15)) (write c))
+    → 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845