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

Author

Christian G. Bower, Jan 21 2008

Keywords

• nonn

References

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

Links

• 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

Programs

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 *)

Formula

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