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topynate comments on Confound it! Correlation is (usually) not causation! But why not? - LessWrong
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There's an asymptotic approximation in the OEIS: a(n) ~ n!2^(n(n-1)/2)/(M*p^n), with M and p constants. So log(a(n)) = O(n^2), as opposed to log(2^n) = O(n), log(n!) = O(n log(n)), log(n^n) = O(n log(n)).