0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

B. Bollobas, Modern Graph Theory, Springer, 1998, p. 290.

J. Riordan, Forests of labeled trees, J. Combin. Theory, 5 (1968), 90-103.

L. Takacs, On the number of distinct forests, SIAM J. Discrete Math., 3 (1990), 574-581.

Wright, E. M., A relationship between two sequences, Proc. London Math. Soc. (3) 17 (1967) 296-304.

T. D. Noe, Table of n, a(n) for n=0..100

David Callan, A Combinatorial Derivation of the Number of Labeled Forests, J. Integer Seqs., Vol. 6, 2003.

Huantian Cao, AutoGF: An Automated System to Calculate Coefficients of Generating Functions.

J. Pitman, Coalescent Random Forests, J. Combin. Theory, A85 (1999), 165-193.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 132

E.g.f.: exp( Sum_{n>=1} n^(n-2)*x^n/n! ). This implies (by a theorem of Wright) that a(n) ~ exp(1/2)*n^(n-2). - N. J. A. Sloane (njas(AT)research.att.com), May 12 2008 [Corrected by Philippe Flajolet, Aug 17 2008]

E.g.f.: exp(T - T^2/2), where T = T(x) = Sum_{ n>=1} n^(n-1)*x^n/n! is Euler's tree function (see A000169). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 12 2001

Shifts 1 place left under the hyperbinomial transform (cf. A088956). - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 03 2003

a(0) = 1, a(n) = Sum_{j=0..n-1} C(n-1,j) (j+1)^(j-1) a(n-1-j) if n>1. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 15 2008]

exp(x+x^2+add(n^(n-2)*x^n/n!, n=3..50));

a:= proc(n) option remember; if n=0 then 1 else add (binomial (n-1, j) *(j+1)^(j-1) *a(n-1-j), j=0..n-1) fi end: seq (a(n), n=0..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 15 2008]

(PARI) a(n)=if(n<0, 0, sum(m=0, n, sum(j=0, m, binomial(m, j)*binomial(n-1, n-m-j)*n^(n-m-j)*(m+j)!/(-2)^j)/m!))

Cf. A088956. Row sums of A138464.

Sequence in context: A145159 A084552 A094664 this_sequence A000366 A106211 A014058

Adjacent sequences: A001855 A001856 A001857 this_sequence A001859 A001860 A001861

nonn,easy,eigen

N. J. A. Sloane (njas(AT)research.att.com) and Simon Plouffe (simon.plouffe(AT)gmail.com)

PARI code and more terms from Michael Somos, Aug 22, 2002.