Hi Damien, | So, I'm having to calculate 'n choose k' an awful lot. At | the moment I've got this: | | comb :: Integer -> Integer -> Integer | comb m 0 = 1 | comb m n = (numerator(toRational (fact m) / toRational (fact | n * fact (m-n)))) | | where fact is a memoized factorial function. It's not | perfectly memoized, though; I use lists, since that's easier | by default. They should be arrays, and possibly just | changing that would speed comb up a lot. (Comb is currently | 40% of runtime, fact is 23%.) But I think it should be | possible to speed up comb itself, too. If you're looking to calculate memoized n choose k, then I'd suggest looking at the following. First, where do the n choose k numbers come from? Forget factorial! Think Pascal's triangle! pascal :: [[Integer]] pascal = iterate (\row -> zipWith (+) ([0] ++ row) (row ++ [0])) [1] Now we can define a variant of your comb function like this: comb :: Int -> Int -> Integer comb n m = pascal !! n !! m (Add an extra line if you want comb to work for values outside the range: 0 <= m <= n. You could also replace the rows of the triangle with arrays, if you want. No factorials, multiplies, or divides here, and natural memoization ...) | comb is only called from here: | sumbn n = sum [ bernoulli i * fromIntegral(comb (n+1) i) | i | <- [0 .. n-1] ] In that case, you can take further advantage of using Pascal's triangle by recognizing that numbers of the form (comb (n+1) i) are just the entries in the (n+1)th row. (All but the last two, for reasons I don't understand ... did you possibly want [0..n+1]?) So we get the following definition: sumbn n = sum [ bernoulli i * fromIntegral c | (i,c) <- zip [0..n-1] (pascal!!(n+1)) ] Actually, I prefer the following version that introduces an explicit dot product operator: sumbn n = take n (map bernoulli [0..]) `dot` (pascal!!(n+1)) dot xs ys = sum (zipWith (*) xs ys) I don't have your setup to test the performance of these definitions, but I'd be curious to know how they fare. Even if they turn out to be slower, I thought these definitions were interesting and different enough to justify sharing ... All the best, Mark