OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2135
Mathematics Stack Exchange Counting free trees from rooted trees.
FORMULA
O.g.f.: R(x) + R(x)^2/2 + R(x^2)/2 where R(x) is the o.g.f. for A000081.
MAPLE
b:= proc(n) option remember; `if`(n<2, n, (add(b(n-j)*add(
d*b(d), d=numtheory[divisors](j)), j=1..n-1))/(n-1))
end:
a:= n-> b(n)+add(b(j)*b(n-j), j=0..n)/2+`if`(n::even, b(n/2)/2, 0):
seq(a(n), n=0..31); # Alois P. Heinz, Feb 17 2024
MATHEMATICA
nn = 25; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[
0 == Series[f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x];
r[x_] := Sum[a[n] x^n, {n, 0, nn}] /. sol; CoefficientList[Series[r[x] + r[x]^2/2 + r[x^2]/2, {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jul 06 2020
STATUS
approved