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

0,3

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 = 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

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 *)

Crossrefs

Column k=10 of A242249.

Sequence in context: A087603 A292837 A261802 * A235340 A306034 A129460

Adjacent sequences: A246236 A246237 A246238 * A246240 A246241 A246242

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved