A136793 Number of unlabeled rooted trees with n 4-colored nodes.

4, 16, 104, 752, 5996, 50512, 444256, 4027360, 37383044, 353486320, 3393093696, 32976302800, 323839605124, 3208549483216, 32033691247528, 321955764477936, 3254812520854980, 33075467402453872, 337670437247448728, 3461635652745799136, 35620112071990294784

Offset

1,1

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).

Links

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

L. Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 (2018)

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Formula

Shifts left and divides by 4 under EULER transform. a(n) = A136794(n)*2 = A052763(n)*4.

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n*4, (add(add(d*
      a(d), d=divisors(j))*a(n-j), j=1..n-1))/(n-1))
    end:
seq(a(n), n=1..25);  # Alois P. Heinz, May 16 2014

Mathematica

a[1] = 4; a[n_] := a[n] = Sum[ Sum[ d*a[d], {d, Divisors[j]}]*a[n-j], {j, 1, n-1}]/(n-1); Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Feb 24 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A332773 A203716 A330537 * A274889 A009630 A318695

Adjacent sequences: A136790 A136791 A136792 * A136794 A136795 A136796

Keyword

nonn

Author

Christian G. Bower, Jan 21 2008

Status

approved