A318230 Number of inequivalent leaf-colorings of binary rooted trees with 2n + 1 nodes.

1, 2, 4, 18, 79, 474, 3166, 24451, 208702, 1958407, 19919811, 217977667, 2547895961, 31638057367, 415388265571, 5743721766718, 83356613617031, 1265900592208029, 20064711719120846, 331153885800672577, 5679210649417608867, 101017359002718628295, 1860460510677429522171

Offset: 0

Author

Gus Wiseman, Aug 21 2018

Keywords

• nonn

Examples

			Inequivalent representatives of the a(3) = 18 leaf-colorings of binary rooted trees with 7 nodes:
  (1(1(11)))  ((11)(11))
  (1(1(12)))  ((11)(12))
  (1(1(22)))  ((11)(22))
  (1(1(23)))  ((11)(23))
  (1(2(11)))  ((12)(12))
  (1(2(12)))  ((12)(13))
  (1(2(13)))  ((12)(34))
  (1(2(22)))
  (1(2(23)))
  (1(2(33)))
  (1(2(34)))
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..49

Crossrefs

Cf. A000081, A001190, A001678, A003238, A004111, A111299, A290689, A304486.

Cf. A318226, A318227, A318228, A318229, A318231, A318234, A319590, A339645.

Programs

PARI

\\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, my(p=x*Ser(v[1..n-1])); v[n]=polcoef(p^2 + if(n%2==0, sRaise(p,2)), n)/2); x*Ser(v)}
InequivalentColoringsSeq(cycleIndexSeries(20)) \\ Andrew Howroyd, Dec 11 2020

Extensions

Terms a(5) and beyond from Andrew Howroyd, Dec 10 2020