A006871 Exponentiation of g.f. for rooted trees.

1, 2, 6, 22, 95, 470, 2618, 16159, 109177, 799959, 6309111, 53230208, 477941835, 4546562149, 45646689381, 482052312792, 5338922526947, 61851205026759, 747755335385701, 9413952961001366, 123184994320876476, 1672494478592315483, 23523730530581660635

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Index entries for sequences related to rooted trees

Maple

b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; unapply(add(b(k)*x^k/k!, k=1..n), x) end: a:= n-> coeff(series(exp(B(n+1)(x)), x=0, n+2), x, n+1)*(n+1)!: seq(a(n), n=0..20); # Alois P. Heinz, Aug 22 2008
# second Maple program:
with(numtheory):
g:= proc(n) option remember; `if`(n<=1, n, (add(add(d*
      g(d), d=divisors(j))*g(n-j), j=1..n-1))/(n-1))
    end:
b:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1)*g(j)*b(n-j), j=1..n))
    end:
a:= n-> b(n+1):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 18 2015

Mathematica

b[n_] := b[n] = If[n <= 1, n, Sum[k*b[k]*s[n-1, k], {k, 1, n-1}]/(n-1)]; s[n_, k_] := s[n, k] = Sum[b[n+1-j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Function[x, Evaluate @ Sum[b[k]*x^k/k!, {k, 1, n}]]; a[n_] := Coefficient[Series[Exp[B[n+1][x]], {x, 0, n+2}], x, n+1]*(n+1)!; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)

Crossrefs

Cf. A000081.

Sequence in context: A093793 A087959 A292096 * A268699 A253948 A248836

Adjacent sequences: A006868 A006869 A006870 * A006872 A006873 A006874

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved