A246239 Number of rooted trees with n nodes and 10-colored non-root nodes.

0, 1, 10, 155, 2770, 54465, 1136402, 24723000, 554540590, 12732651160, 297795974970, 7069820334023, 169926110309380, 4126836768095315, 101114499262401970, 2496432769621336865, 62045482307629427354, 1551083997228106913910, 38976793037598171500920

Offset: 0

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

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.

Crossrefs

Column k=10 of A242249.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, (add(add(d*
      a(d), d=divisors(j))*a(n-j)*10, 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]*10, {j, 1, n-1}]/(n-1)];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 23 2019, from Maple *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = 27.3718979186642404090999595957978919036..., c = 0.04017690459295003799582996890456677644... . - Vaclav Kotesovec, Aug 26 2014

G.f. A(x) satisfies: A(x) = x*exp(10*Sum_{k>=1} A(x^k)/k). - Ilya Gutkovskiy, Mar 20 2018