cp's OEIS Frontend

A320173 Number of inequivalent colorings of series-reduced balanced rooted trees with n leaves.

%I A320173 #8 Dec 14 2020 14:18:33
%S A320173 1,2,3,12,23,84,204,830,2940,13397,58794,283132,1377302,7087164,
%T A320173 37654377,209943842,1226495407,7579549767,49541194089,341964495985,
%U A320173 2476907459261,18703210872343,146284738788714,1179199861398539,9760466433602510,82758834102114911,717807201648148643
%N A320173 Number of inequivalent colorings of series-reduced balanced rooted trees with n leaves.
%C A320173 A rooted tree is series-reduced if every non-leaf node has at least two branches, and balanced if all leaves are the same distance from the root.
%e A320173 Inequivalent representatives of the a(1) = 1 through a(5) = 23 colorings:
%e A320173   1  (11)  (111)    (1111)      (11111)
%e A320173      (12)  (112)    (1112)      (11112)
%e A320173            (123)    (1122)      (11122)
%e A320173                     (1123)      (11123)
%e A320173                     (1234)      (11223)
%e A320173                   ((11)(11))    (11234)
%e A320173                   ((11)(12))    (12345)
%e A320173                   ((11)(22))  ((11)(111))
%e A320173                   ((11)(23))  ((11)(112))
%e A320173                   ((12)(12))  ((11)(122))
%e A320173                   ((12)(13))  ((11)(123))
%e A320173                   ((12)(34))  ((11)(223))
%e A320173                               ((11)(234))
%e A320173                               ((12)(111))
%e A320173                               ((12)(112))
%e A320173                               ((12)(113))
%e A320173                               ((12)(123))
%e A320173                               ((12)(134))
%e A320173                               ((12)(345))
%e A320173                               ((13)(122))
%e A320173                               ((22)(111))
%e A320173                               ((23)(111))
%e A320173                               ((23)(114))
%o A320173 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A320173 cycleIndexSeries(n)={my(p=x*sv(1) + O(x*x^n), q=0); while(p, q+=p; p=sEulerT(p)-1-p); q}
%o A320173 InequivalentColoringsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 11 2020
%Y A320173 Cf. A000669, A005804, A048816, A079500, A119262, A120803, A141268, A244925, A319312.
%Y A320173 Cf. A320154, A320155, A320160, A320174, A320175, A320179, A339645.
%K A320173 nonn
%O A320173 1,2
%A A320173 _Gus Wiseman_, Oct 07 2018
%E A320173 Terms a(8) and beyond from _Andrew Howroyd_, Dec 11 2020