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1, 4, 25, 216, 2401, 32768, 531441, 10000000, 214358881, 5159780352, 137858491849, 4049565169664, 129746337890625, 4503599627370496, 168377826559400929, 6746640616477458432, 288441413567621167681
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n-2) = number of trees with n+1 unlabeled vertices and n labeled edges for n > 1 (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
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REFERENCES
| 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.
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LINKS
| 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
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FORMULA
| 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
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MAPLE
| 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]
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MATHEMATICA
| Table[ (n+3)^n, {n, 0, 18} ]
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CROSSREFS
| Cf. A000169, A000272, A000312, A007778, A008785-A008791.
Contribution from Thomas Wieder (thomas.wieder(AT)t-online.de), Feb 07 2010: (Start)
for n to 6 do ST := [seq(seq(i, j = 1 .. n+2), i = 1 .. n)]; PST := powerset(ST);
Result[n] := nops(PST) end do; seq(Result[n], n = 1 .. 6) (End)
Sequence in context: A049118 A047733 A198198 * A060911 A060912 A050386
Adjacent sequences: A007827 A007828 A007829 * A007831 A007832 A007833
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Peter Cameron [ P.J.Cameron(AT)qmw.ac.uk ]
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EXTENSIONS
| Corrected the comment about number of trees with n+1 unlabeled vertices and n labeled edges. This number is a(n-2) and not a(n+2) as originally stated.
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