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

0,2

Links

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

Example

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)))

Prog

(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

Crossrefs

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

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

Sequence in context: A014448 A277033 A295767 * A075836 A295370 A292280

Adjacent sequences: A318227 A318228 A318229 * A318231 A318232 A318233

Keyword

nonn

Author

Gus Wiseman, Aug 21 2018

Extensions

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

Status

approved