OFFSET
1,2
COMMENTS
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.
EXAMPLE
Non-isomorphic representatives of the a(3) = 14 trees:
((1)((1)(1))) ((1)((1)(2))) ((1)((2)(3))) ((2)((1)(1)))
((1)(1)(1)) ((1)(1)(2)) ((1)(2)(3)) ((2)(1,1))
((1)(1,1)) ((1)(1,2)) ((1)(2,3))
(1,1,1) (1,1,2) (1,2,3)
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
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)}
InequivalentColoringsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 13 2020
CROSSREFS
The version where leaves are atoms is A318231.
The case with sets as leaves is A330624.
The case with disjoint sets as leaves is A141268.
The singleton-reduced version is A330470.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 21 2019
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Dec 13 2020
STATUS
approved