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A330470 Number of non-isomorphic series/singleton-reduced rooted trees on a multiset of size n. 12
1, 1, 2, 7, 39, 236, 1836, 16123, 162008, 1802945, 22012335, 291290460, 4144907830, 62986968311, 1016584428612, 17344929138791, 311618472138440, 5875109147135658, 115894178676866576, 2385755803919949337, 51133201045333895149, 1138659323863266945177, 26296042933904490636133 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A series/singleton-reduced rooted tree on a multiset m is either the multiset m itself or a sequence of series/singleton-reduced rooted trees, one on each part of a multiset partition of m that is neither minimal (all singletons) nor maximal (only one part).
LINKS
EXAMPLE
Non-isomorphic representatives of the a(4) = 39 trees, with singleton leaves (x) replaced by just x:
(1111) (1112) (1122) (1123) (1234)
(1(111)) (1(112)) (1(122)) (1(123)) (1(234))
(11(11)) (11(12)) (11(22)) (11(23)) (12(34))
((11)(11)) (12(11)) (12(12)) (12(13)) ((12)(34))
(1(1(11))) (2(111)) ((11)(22)) (2(113)) (1(2(34)))
((11)(12)) (1(1(22))) (23(11))
(1(1(12))) ((12)(12)) ((11)(23))
(1(2(11))) (1(2(12))) (1(1(23)))
(2(1(11))) ((12)(13))
(1(2(13)))
(2(1(13)))
(2(3(11)))
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, v[n] = polcoef( sEulerT(x*Ser(v[1..n])), n )); x*Ser(v)}
InequivalentColoringsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 11 2020
CROSSREFS
The case with all atoms equal or all atoms different is A000669.
Not requiring singleton-reduction gives A330465.
Labeled versions are A316651 (normal orderless) and A330471 (strongly normal).
The case where the leaves are sets is A330626.
Row sums of A339645.
Sequence in context: A119602 A121752 A054133 * A364336 A266310 A032118
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 22 2019
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Dec 11 2020
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)