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A318231 Number of inequivalent leaf-colorings of series-reduced rooted trees with n nodes. 12
1, 0, 2, 3, 9, 23, 73, 229, 796, 2891, 11118, 44695, 187825, 820320, 3716501, 17413308, 84209071, 419461933, 2148673503, 11301526295, 60956491070, 336744177291, 1903317319015, 10995856040076, 64873456288903, 390544727861462, 2397255454976268, 14993279955728851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

In a series-reduced rooted tree, every non-leaf node has at least two branches.

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

Inequivalent representatives of the a(6) = 23 leaf-colorings:

  (11(11))  (1(111))  (11111)

  (11(12))  (1(112))  (11112)

  (11(22))  (1(122))  (11122)

  (11(23))  (1(123))  (11123)

  (12(11))  (1(222))  (11223)

  (12(12))  (1(223))  (11234)

  (12(13))  (1(234))  (12345)

  (12(33))

  (12(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, v[n] = polcoef( sEulerT(x*Ser(concat(v[1..n-2], [0]))), n-1 )); x*Ser(v)}

InequivalentColoringsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 11 2020

CROSSREFS

Cf. A000081, A001190, A001678, A003238, A004111, A290689, A291636, A304486.

Cf. A318226, A318227, A318228, A318229, A318230, A318234, A339645, A339648.

Sequence in context: A227252 A274495 A299705 * A242271 A056198 A143742

Adjacent sequences:  A318228 A318229 A318230 * A318232 A318233 A318234

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 21 2018

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Dec 11 2020

STATUS

approved

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Last modified February 28 17:08 EST 2021. Contains 341707 sequences. (Running on oeis4.)