Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Dec 13 2020 17:26:35
%S 1,0,2,3,9,23,73,229,796,2891,11118,44695,187825,820320,3716501,
%T 17413308,84209071,419461933,2148673503,11301526295,60956491070,
%U 336744177291,1903317319015,10995856040076,64873456288903,390544727861462,2397255454976268,14993279955728851
%N Number of inequivalent leaf-colorings of series-reduced rooted trees with n nodes.
%C In a series-reduced rooted tree, every non-leaf node has at least two branches.
%e Inequivalent representatives of the a(6) = 23 leaf-colorings:
%e (11(11)) (1(111)) (11111)
%e (11(12)) (1(112)) (11112)
%e (11(22)) (1(122)) (11122)
%e (11(23)) (1(123)) (11123)
%e (12(11)) (1(222)) (11223)
%e (12(12)) (1(223)) (11234)
%e (12(13)) (1(234)) (12345)
%e (12(33))
%e (12(34))
%o (PARI) \\ See links in A339645 for combinatorial species functions.
%o 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 InequivalentColoringsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 11 2020
%Y Cf. A000081, A001190, A001678, A003238, A004111, A290689, A291636, A304486.
%Y Cf. A318226, A318227, A318228, A318229, A318230, A318234, A339645, A339648.
%K nonn
%O 1,3
%A _Gus Wiseman_, Aug 21 2018
%E Terms a(8) and beyond from _Andrew Howroyd_, Dec 11 2020