Search: id:A007830
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%I A007830
%S A007830 1,4,25,216,2401,32768,531441,10000000,214358881,5159780352,
%T A007830 137858491849,4049565169664,129746337890625,4503599627370496,
%U A007830 168377826559400929,6746640616477458432,288441413567621167681
%N A007830 (n+3)^n.
%C A007830 a(n+2) = number of trees with n+1 unlabeled vertices and n labeled edges 
               (Christian G. Bower, 12/99).
%C A007830 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
%D A007830 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.
%D A007830 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 5.27.
%H A007830 T. D. Noe, <a href="b007830.txt">Table of n, a(n) for n=0..100</a>
%H A007830 P. J. Cameron, <a href="http://www.combinatorics.org/Volume_2/volume2.html#R4">
               Counting two-graphs related to trees</a>, Elec. J. Combin., Vol. 
               2, #R4.
%H A007830 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A007830 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A007830 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
%F A007830 E.g.f.: -LambertW(-x)^3/(1+LambertW(-x))/x^3. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Nov 07 2003
%p A007830 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)
%p A007830 seq(mul(n, k=4..n), n=3..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 15 2008
%p A007830 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
%p A007830 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]
%p A007830 with(finance):seq(futurevalue(1,n+2,n), n=0..16);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 24 2009]
%t A007830 Table[ (n+3)^n, {n, 0, 18} ]
%Y A007830 Cf. A000169, A000272, A000312, A007778, A008785-A008791.
%Y A007830 Sequence in context: A038174 A049118 A047733 this_sequence A060911 A060912 
               A050386
%Y A007830 Adjacent sequences: A007827 A007828 A007829 this_sequence A007831 A007832 
               A007833
%K A007830 nonn,nice,easy
%O A007830 0,2
%A A007830 Peter Cameron [ P.J.Cameron(AT)qmw.ac.uk ]

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