This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A144757 #14 Sep 20 2019 09:00:20
%S A144757 1,1,1,1,2,1,2,1,2,1,6,1,2,2,5,1,6,1,6,2,2,1,20,1,2,2,6,1,12,1,14,2,2,
%T A144757 2,30,1,2,2,20,1,12,1,6,6,2,1,70,1,6,2,6,1,20,2,20,2,2,1,60,1,2,6,42,
%U A144757 2,12,1,6,2,12,1,140,1,2,6,6,2,12,1,70,5,2,1,60,2,2,2,20,1,60,2,6,2,2,2,252
%N A144757 Number of factor trees for n.
%C A144757 A factor tree for n is a binary tree, with the root labeled with n and the terminal nodes labeled with primes, such that each non-terminal node is the product of its two child nodes. This is the number of prime factorizations of n, ignoring the commutativity and associativity of multiplication.
%H A144757 Reinhard Zumkeller, <a href="/A144757/b144757.txt">Table of n, a(n) for n = 2..10000</a>
%F A144757 a(n) = A000108(A001222(n)-1) * A008480(n).
%e A144757 a(12)=6 because 12 can be factored as (2*2)*3, (2*3)*2, (3*2)*2, 2*(2*3), 2*(3*2) and 3*(2*2).
%t A144757 a8480[n_] := With[{f = FactorInteger[n][[All, 2]]}, Total[f]!/Times @@ (f!)];
%t A144757 a[n_] := CatalanNumber[PrimeOmega[n] - 1] * a8480[n];
%t A144757 a /@ Range[2, 100] (* _Jean-François Alcover_, Sep 20 2019 *)
%o A144757 (Haskell)
%o A144757 a144757 n = a000108 (a001222 n - 1) * a008480 n
%o A144757 -- _Reinhard Zumkeller_, Nov 19 2015
%o A144757 (PARI) seq(n)={my(v=vector(n)); for(n=2, n, v[n] = isprime(n) + sumdiv(n, d, v[d]*v[n/d])); v[2..n]} \\ _Andrew Howroyd_, Nov 17 2018
%o A144757 (PARI) a(n)={if(n>=2, my(sig=factor(n)[,2]); my(t=vecsum(sig)-1); binomial(2*t, t)*t!/vecprod(apply(k->k!, sig)), 0)} \\ _Andrew Howroyd_, Nov 17 2018
%Y A144757 Cf. A000108, A001222, A008480, A277120.
%K A144757 easy,nonn
%O A144757 2,5
%A A144757 _David Radcliffe_, Sep 20 2008