A038052 Number of labeled trees of nonempty sets with n points. (Each node is a set of 1 or more points.)

1, 1, 2, 7, 42, 376, 4513, 68090, 1238968, 26416729, 646140364, 17837852044, 548713088399, 18612963873492, 690271321314292, 27785827303491579, 1206582732097720126, 56224025231569020724, 2798445211000659147033, 148178324442139816854902, 8317074395027724691495980

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..379 (first 101 terms from T. D. Noe)

Index entries for sequences related to trees

Formula

E.g.f.: B(e^x-1) where B is e.g.f. of A000272.

a(n) = Sum_{k=1..n} Stirling2(n, k)*k^(k-2). - Vladeta Jovovic, Sep 20 2003

a(n) ~ (1+exp(1))^(3/2) * n^(n-2) / (exp(n) * (log(1+exp(-1)))^(n-3/2)). - Vaclav Kotesovec, Feb 17 2017

Maple

b:= proc(n, m) option remember; `if`(n=0,
      m^max(0, m-2), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..21);  # Alois P. Heinz, Jul 16 2022

Mathematica

a[0] = 1; a[n_] := Sum[StirlingS2[n, k]*k^(k - 2), {k, 1, n}]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Sep 09 2013, after Vladeta Jovovic *)

Crossrefs

Cf. A036250, A048802.

Sequence in context: A317349 A158840 A359717 * A371079 A066383 A011802

Adjacent sequences: A038049 A038050 A038051 * A038053 A038054 A038055

Keyword

nonn,nice,easy

Author

Christian G. Bower, Jan 04 1999

Status

approved