A246237 Number of rooted trees with n nodes and 8-colored non-root nodes.

0, 1, 8, 100, 1432, 22570, 377320, 6578116, 118238600, 2175619923, 40778137032, 775828919936, 14944103723856, 290858342628604, 5711285455910096, 113005043943326568, 2250850657029983808, 45095294493866921469, 908159403846847306568, 18373705506139825769712

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Loïc Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA], 2018.

Formula

a(n) ~ c * d^n / n^(3/2), where d = 21.9366222112987115910888213763759058905..., c = 0.05031446862451857508141944218348994381... . - Vaclav Kotesovec, Aug 26 2014

G.f. A(x) satisfies: A(x) = x*exp(8*Sum_{k>=1} A(x^k)/k). - Ilya Gutkovskiy, Mar 20 2018

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, (add(add(d*
      a(d), d=divisors(j))*a(n-j)*8, j=1..n-1))/(n-1))
    end:
seq(a(n), n=0..25);

Mathematica

a[n_] := a[n] = If[n<2, n, Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j]*8, {j, 1, n-1}]/(n-1)];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 23 2019, from Maple *)

Crossrefs

Column k=8 of A242249.

Sequence in context: A144072 A261800 A208705 * A234513 A251686 A306032

Adjacent sequences: A246234 A246235 A246236 * A246238 A246239 A246240

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved