cp's OEIS Frontend

A330465 Number of non-isomorphic series-reduced rooted trees whose leaves are multisets with a total of n elements.

%I A330465 #12 Dec 14 2020 01:37:10
%S A330465 1,4,14,87,608,5573,57876,687938,9058892,130851823,2048654450,
%T A330465 34488422057,620046639452,11839393796270,238984150459124,
%U A330465 5079583100918338,113299159314626360,2644085918303683758,64393240540265515110,1632731130253043991252,43013015553755764179000
%N A330465 Number of non-isomorphic series-reduced rooted trees whose leaves are multisets with a total of n elements.
%C A330465 Also inequivalent leaf-colorings of phylogenetic rooted trees with n labels. A phylogenetic rooted tree is a series-reduced rooted tree whose leaves are (usually disjoint) sets.
%e A330465 Non-isomorphic representatives of the a(3) = 14 trees:
%e A330465   ((1)((1)(1)))  ((1)((1)(2)))  ((1)((2)(3)))  ((2)((1)(1)))
%e A330465   ((1)(1)(1))    ((1)(1)(2))    ((1)(2)(3))    ((2)(1,1))
%e A330465   ((1)(1,1))     ((1)(1,2))     ((1)(2,3))
%e A330465   (1,1,1)        (1,1,2)        (1,2,3)
%o A330465 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A330465 cycleIndexSeries(n)={my(v=vector(n), p=sEulerT(x*sv(1) + O(x*x^n))); v[1]=sv(1); for(n=2, #v, v[n] = polcoef( sEulerT(x*Ser(v[1..n])), n ) + polcoef(p,n)); x*Ser(v)}
%o A330465 InequivalentColoringsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 13 2020
%Y A330465 The version where leaves are atoms is A318231.
%Y A330465 The case with sets as leaves is A330624.
%Y A330465 The case with disjoint sets as leaves is A141268.
%Y A330465 Labeled versions are A330467 (strongly normal) and A330469 (normal).
%Y A330465 The singleton-reduced version is A330470.
%Y A330465 Cf. A000311, A000669, A004114, A005804, A007716, A281118, A289501, A292504, A316651, A316652, A318812, A319312, A330471, A330474, A330625, A339645.
%K A330465 nonn
%O A330465 1,2
%A A330465 _Gus Wiseman_, Dec 21 2019
%E A330465 Terms a(7) and beyond from _Andrew Howroyd_, Dec 13 2020