Data commit

Task/Pascals-triangle/Lambdatalk/pascals-triangle.lambdatalk

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+1) Based on this expression of pascalian binomial:
+
+     Cnp = [n*(n-1)...(n-p+1)]/[p*(p-1)...2*1]
+
+2) we define the following function:
+
+{def C
+ {lambda {:n :p}
+  {/ {* {S.serie :n {- :n :p -1} -1}}
+     {* {S.serie :p 1 -1}}}}}
+
+{C 16 8}
+-> 12870
+
+3) Writing
+
+1{S.map {lambda {:n} {br}1
+ {S.map {C :n} {S.serie 1 {- :n 1}}} 1}
+               {S.serie 2 16}}
+displays:
+
+1
+1 2 1
+1 3 3 1
+1 4 6 4 1
+1 5 10 10 5 1
+1 6 15 20 15 6 1
+1 7 21 35 35 21 7 1
+1 8 28 56 70 56 28 8 1
+1 9 36 84 126 126 84 36 9 1
+1 10 45 120 210 252 210 120 45 10 1
+1 11 55 165 330 462 462 330 165 55 11 1
+1 12 66 220 495 792 924 792 495 220 66 12 1
+1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
+1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1
+1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1
+1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1