A006790 Exponentiation of e.g.f. for trees A000055(n-1).

1, 2, 5, 15, 53, 211, 938, 4582, 24349, 139671, 858745, 5628789, 39145021, 287667582, 2226033629, 18082308403, 153770703339, 1365631349757, 12638233544989, 121640399661294, 1215438543434225, 12587691428792115

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Index entries for sequences related to trees

Crossrefs

Cf. A000055.

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n<=1, n, add(add(d*
      b(d), d=divisors(j))*b(n-j), j=1..n-1)/(n-1))
    end:
t:= proc(n) option remember; `if`(n=0, 1, b(n)-(add(b(k)
      *b(n-k), k=0..n)-`if`(irem(n, 2)=0, b(n/2), 0))/2)
    end:
g:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1) *t(j-1) *g(n-j), j=1..n))
    end:
a:= n-> g(n+1):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 16 2015

Mathematica

b[n_] := b[n] = If[n <= 1, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]; t[n_] := t[n] = If[n==0, 1, b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[ Mod[n, 2] == 0, b[n/2], 0])/2]; g[n_] := g[n] = If[n==0, 1, Sum[Binomial[n-1, j-1] *t[j-1]*g[n-j], {j, 1, n}]]; a[n_] := g[n+1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 30 2015, after Alois P. Heinz *)