login
A309994
Number of forests of rooted trees with 2n colored nodes using exactly n colors.
2
1, 2, 89, 14845, 5613775, 3809941836, 4073969863427, 6316651717425358, 13407079935176225215, 37344967651943608528498, 132181958309965092862822183, 579566807739313784043087337938, 3083812115454145185391757131500066, 19577110356940490275990571617295644659
OFFSET
0,2
LINKS
FORMULA
a(n) = A256064(2*n+1,n).
MAPLE
b:= proc(n, k) option remember; `if`(n<2, n, (add(add(d*b(d, k),
d=numtheory[divisors](j))*b(n-j, k)*k, j=1..n-1))/(n-1))
end:
a:= n-> add(b(2*n+1, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..15);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n < 2, n, Sum[Sum[d*b[d, k], {d, Divisors[j]}]*b[n-j, k]*k, {j, 1, n-1}]/(n-1)];
a[n_] := Sum[b[2*n+1, n-i]*(-1)^i*Binomial[n, i], {i, 0, n}];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Sep 15 2022, after Alois P. Heinz *)
CROSSREFS
Cf. A256064.
Sequence in context: A246871 A024239 A338734 * A339581 A256962 A266807
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 26 2019
STATUS
approved