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A318230
Number of inequivalent leaf-colorings of binary rooted trees with 2n + 1 nodes.
7
1, 2, 4, 18, 79, 474, 3166, 24451, 208702, 1958407, 19919811, 217977667, 2547895961, 31638057367, 415388265571, 5743721766718, 83356613617031, 1265900592208029, 20064711719120846, 331153885800672577, 5679210649417608867, 101017359002718628295, 1860460510677429522171
OFFSET
0,2
LINKS
EXAMPLE
Inequivalent representatives of the a(3) = 18 leaf-colorings of binary rooted trees with 7 nodes:
(1(1(11))) ((11)(11))
(1(1(12))) ((11)(12))
(1(1(22))) ((11)(22))
(1(1(23))) ((11)(23))
(1(2(11))) ((12)(12))
(1(2(12))) ((12)(13))
(1(2(13))) ((12)(34))
(1(2(22)))
(1(2(23)))
(1(2(33)))
(1(2(34)))
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
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)}
InequivalentColoringsSeq(cycleIndexSeries(20)) \\ Andrew Howroyd, Dec 11 2020
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 21 2018
EXTENSIONS
Terms a(5) and beyond from Andrew Howroyd, Dec 10 2020
STATUS
approved