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 A318231 #10 Dec 13 2020 17:26:35
%S A318231 1,0,2,3,9,23,73,229,796,2891,11118,44695,187825,820320,3716501,
%T A318231 17413308,84209071,419461933,2148673503,11301526295,60956491070,
%U A318231 336744177291,1903317319015,10995856040076,64873456288903,390544727861462,2397255454976268,14993279955728851
%N A318231 Number of inequivalent leaf-colorings of series-reduced rooted trees with n nodes.
%C A318231 In a series-reduced rooted tree, every non-leaf node has at least two branches.
%e A318231 Inequivalent representatives of the a(6) = 23 leaf-colorings:
%e A318231 (11(11)) (1(111)) (11111)
%e A318231 (11(12)) (1(112)) (11112)
%e A318231 (11(22)) (1(122)) (11122)
%e A318231 (11(23)) (1(123)) (11123)
%e A318231 (12(11)) (1(222)) (11223)
%e A318231 (12(12)) (1(223)) (11234)
%e A318231 (12(13)) (1(234)) (12345)
%e A318231 (12(33))
%e A318231 (12(34))
%o A318231 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A318231 cycleIndexSeries(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, v[n] = polcoef( sEulerT(x*Ser(concat(v[1..n-2], [0]))), n-1 )); x*Ser(v)}
%o A318231 InequivalentColoringsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 11 2020
%Y A318231 Cf. A000081, A001190, A001678, A003238, A004111, A290689, A291636, A304486.
%Y A318231 Cf. A318226, A318227, A318228, A318229, A318230, A318234, A339645, A339648.
%K A318231 nonn
%O A318231 1,3
%A A318231 _Gus Wiseman_, Aug 21 2018
%E A318231 Terms a(8) and beyond from _Andrew Howroyd_, Dec 11 2020