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 A320293 #8 Oct 25 2018 22:21:30
%S A320293 0,1,1,3,3,9,11,30,45,112,195,475,901,2136,4349,10156,21565,50003,
%T A320293 109325,252761,563785,1303296,2948555,6826494,15604053,36210591,
%U A320293 83415487,194094257,449813607,1049555795,2444027917,5718195984,13367881473,31357008065,73546933115
%N A320293 Number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of n with no 1's.
%C A320293 Also phylogenetic trees on integer partitions of n with no 1's.
%H A320293 Andrew Howroyd, <a href="/A320293/b320293.txt">Table of n, a(n) for n = 1..500</a>
%e A320293 The a(2) = 1 through a(7) = 11 trees:
%e A320293 (2) (3) (4) (5) (6) (7)
%e A320293 (22) (32) (33) (43)
%e A320293 ((2)(2)) ((2)(3)) (42) (52)
%e A320293 (222) (322)
%e A320293 ((2)(4)) ((2)(5))
%e A320293 ((3)(3)) ((3)(4))
%e A320293 ((2)(22)) ((2)(23))
%e A320293 ((2)(2)(2)) ((3)(22))
%e A320293 ((2)((2)(2))) ((2)(2)(3))
%e A320293 ((2)((2)(3)))
%e A320293 ((3)((2)(2)))
%o A320293 (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A320293 seq(n)={my(p=1/prod(k=2, n, 1 - x^k + O(x*x^n)), v=vector(n)); for(n=1, n, v[n]=polcoef(p, n) + EulerT(v[1..n])[n]); v} \\ _Andrew Howroyd_, Oct 25 2018
%Y A320293 Cf. A000045, A000311, A000669, A002865, A141268, A292504, A300660, A304967, A319312, A320289, A320294, A320295, A320296.
%K A320293 nonn
%O A320293 1,4
%A A320293 _Gus Wiseman_, Oct 09 2018
%E A320293 Terms a(23) and beyond from _Andrew Howroyd_, Oct 25 2018