Bell numbers: Difference between revisions

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 numeric digits max(9, HI*2)                      /*crudely calculate the # decimal digs.*/
 !.=;                       @.= 1                 /*the  FACT  function uses memoization.*/
-     do j=0  for  HI+1;    $= 0;       jm= j-1   /*JM  is used for a shortcut  (below). */
+     do j=0  for  HI+1;    $= (j==0);    jm= j-1 /*JM  is used for a shortcut  (below). */
-     if j==0  then $= 1                          /*use fiat value for the first Bell #. */
+            do k=0  for j;            _= jm-k    /* [↓]  calculate a Bell # the easy way*/
-              else do k=0  for j;       _= jm-k  /* [↓]  calculate a Bell # the easy way*/
+            $= $ + comb(jm,k) * @._              /*COMB≡combination or binomial function*/
-                   $= $ + comb(jm,k) * @._       /*COMB≡combination or binomial function*/
+            end   /*k*/
-                   end   /*k*/
      @.j= $                                      /*assign the Jth Bell number to @ array*/
      if j>=LO  &  j<=HI  then say '    bell('right(j, length(HI) )") = "      $