Catalan numbers for triangulations gambler’s ruin binary…

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Catalan numbers for

  • triangulations
  • gambler’s ruin
  • binary trees
  • trees

…from the Flajolet/Sedgewick coursera analysis of algorithms

Noncrossing partitions 5.svg

in R:

catalan % sum
    }

(This is slow above catalan(10) though, so here’s a memoised version. Then if you want to run above catalan(250) you’ll need to adjust options(expressions=5e3) to something higher; otherwise the nesting of calls goes too deep.)

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