sequence by formula fails on catalan numbers

[katestange]

I know I just put a bunch of issues in on sequence by formula, but I think (?) this one is not the same bug as any of the other ones. This is a formula that should be valid (return an integer). The following formula for the n+1-st Catalan number fails:
factorial(2*(n+1))/factorial(n+2)/factorial(n+1). I've put n+1 so that the factorials are all defined even at n=0. It fails one some big numbers somewhere, where it says they aren't integers, e.g. Uncaught RangeError: The number 477638699.99999994 cannot be converted to a BigInt because it is not an integer

[gwhitney]

Yeah, straight-up dividing factorials is generally a problematic computation strategy: not helpful to generate a huge numerator and a huge denominator and then rely on lots and lots of cancellation. (You might have gotten away with this if bigints were already incorporated in mathjs, but you would still be making your computer work much harder than need be.) Much better to stick with (2n choose n)/(n+1) where the implementation can do all the canceling termwise inside the binomial coefficient, so that the intermediate results don't get anywhere near so big. Then you can get much farther without overflow. In mathjs and hence in our formulas this is combinations(2n, n)/(n+1) (maybe we should link to the mathjs documentation from the frontscope documentation?). But even easier is catalan(n) ;-) (which is already implemented in mathjs, as it happens)

[gwhitney]

I'll leave this up as a bug until we at least get a try-catch in the right place.

[gwhitney]

Should be moot once #343 is addressed.