A330465 Number of non-isomorphic series-reduced rooted trees whose leaves are multisets with a total of n elements.

1, 4, 14, 87, 608, 5573, 57876, 687938, 9058892, 130851823, 2048654450, 34488422057, 620046639452, 11839393796270, 238984150459124, 5079583100918338, 113299159314626360, 2644085918303683758, 64393240540265515110, 1632731130253043991252, 43013015553755764179000

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.

Links

Table of n, a(n) for n=1..21.

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.

Labeled versions are A330467 (strongly normal) and A330469 (normal).

The singleton-reduced version is A330470.

Cf. A000311, A000669, A004114, A005804, A007716, A281118, A289501, A292504, A316651, A316652, A318812, A319312, A330471, A330474, A330625, A339645.

Sequence in context: A259353 A339193 A352289 * A202139 A331637 A340024

Adjacent sequences: A330462 A330463 A330464 * A330466 A330467 A330468

Keyword

nonn

Author

Gus Wiseman, Dec 21 2019

Extensions

Terms a(7) and beyond from Andrew Howroyd, Dec 13 2020

Status

approved