A318231 Number of inequivalent leaf-colorings of series-reduced rooted trees with n nodes.

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

Offset: 1

Author

Gus Wiseman, Aug 21 2018

Keywords

• nonn

Comments

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

Examples

			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))
		

Crossrefs

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

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

Programs

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

Extensions

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