0,2

a(n+2) = number of trees with n+1 unlabeled vertices and n labeled edges (Christian G. Bower, 12/99).

a(n) is also the number of nonequivalent primitive meromorphic functions with one pole of order n+3 on a Riemann surface of genus 0 - Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001

M. Shapiro, B.Shapiro and A.Vainshtein - Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs, Amer. Math. Soc. Transl., Vol. 180 (1997), pp. 219-227.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.27.

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

P. J. Cameron, Counting two-graphs related to trees, Elec. J. Combin., Vol. 2, #R4.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Index entries for sequences related to trees

E.g.f. for b(n) = a(n-3): T(x)-(3/4)T^2(x)+(1/6)T^3(x), where T(x) is Euler's tree function (see A000169). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 17 2001

E.g.f.: -LambertW(-x)^3/(1+LambertW(-x))/x^3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 07 2003

T := x->-LambertW(-x); series((T(x))^3/6-3*(T(x))^2/4+T(x), x, 24); #mult. coeff. of x^n by n!, get a(n-3)

seq(mul(n, k=4..n), n=3..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 15 2008

a:=n->mul(denom (1/(n+4)), k=0..n): seq(a(n), n=-1..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2008

a:=n->mul(1+add(1, j=1..n), j=3..n):seq(a(n), n=2..18); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2008]

with(finance):seq(futurevalue(1, n+2, n), n=0..16); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 24 2009]

Table[ (n+3)^n, {n, 0, 18} ]

Cf. A000169, A000272, A000312, A007778, A008785-A008791.

Sequence in context: A038174 A049118 A047733 this_sequence A060911 A060912 A050386

Adjacent sequences: A007827 A007828 A007829 this_sequence A007831 A007832 A007833

nonn,nice,easy

Peter Cameron [ P.J.Cameron(AT)qmw.ac.uk ]