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A318230 Number of inequivalent leaf-colorings of binary rooted trees with 2n + 1 nodes.

%I A318230 #12 Dec 14 2020 14:19:17
%S A318230 1,2,4,18,79,474,3166,24451,208702,1958407,19919811,217977667,
%T A318230 2547895961,31638057367,415388265571,5743721766718,83356613617031,
%U A318230 1265900592208029,20064711719120846,331153885800672577,5679210649417608867,101017359002718628295,1860460510677429522171
%N A318230 Number of inequivalent leaf-colorings of binary rooted trees with 2n + 1 nodes.
%H A318230 Andrew Howroyd, <a href="/A318230/b318230.txt">Table of n, a(n) for n = 0..49</a>
%e A318230 Inequivalent representatives of the a(3) = 18 leaf-colorings of binary rooted trees with 7 nodes:
%e A318230   (1(1(11)))  ((11)(11))
%e A318230   (1(1(12)))  ((11)(12))
%e A318230   (1(1(22)))  ((11)(22))
%e A318230   (1(1(23)))  ((11)(23))
%e A318230   (1(2(11)))  ((12)(12))
%e A318230   (1(2(12)))  ((12)(13))
%e A318230   (1(2(13)))  ((12)(34))
%e A318230   (1(2(22)))
%e A318230   (1(2(23)))
%e A318230   (1(2(33)))
%e A318230   (1(2(34)))
%o A318230 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A318230 cycleIndexSeries(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, my(p=x*Ser(v[1..n-1])); v[n]=polcoef(p^2 + if(n%2==0, sRaise(p,2)), n)/2); x*Ser(v)}
%o A318230 InequivalentColoringsSeq(cycleIndexSeries(20)) \\ _Andrew Howroyd_, Dec 11 2020
%Y A318230 Cf. A000081, A001190, A001678, A003238, A004111, A111299, A290689, A304486.
%Y A318230 Cf. A318226, A318227, A318228, A318229, A318231, A318234, A319590, A339645.
%K A318230 nonn
%O A318230 0,2
%A A318230 _Gus Wiseman_, Aug 21 2018
%E A318230 Terms a(5) and beyond from _Andrew Howroyd_, Dec 10 2020