|
| |
|
|
A001864
|
|
Total height of rooted trees with n labeled nodes.
(Formerly M2138 N0850)
|
|
5
| |
|
|
0, 2, 24, 312, 4720, 82800, 1662024, 37665152, 952401888, 26602156800, 813815035000, 27069937855488, 972940216546896, 37581134047987712, 1552687346633913000, 68331503866677657600, 3191386068123595166656, 157663539876436721860608
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Zvonkine, D., Counting ramified coverings and intersection theory on Hurwitz spaces II (local structure of Hurwitz spaces and combinatorial results). Moscow Mathematical Journal, vol. 7 (2007), no. 1, 135-162.
Zvonkine, D., Enumeration of ramified coverings of the sphere and 2-dimensional gravity, Preprint 2004.
Zvonkine, D., An algebra of power series arising in the intersection theory of moduli spaces of curves and in the enumeration of ramified coverings of the sphere. Preprint 2004.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
J. Riordan and N. J. A. Sloane, Enumeration of rooted trees by total height, J. Austral. Math. Soc., vol. 10 pp. 278-282, 1969.
N. J. A. Sloane, Illustration of terms a(3) and a(4) in A000435
D. Zvonkine, Home Page
D. Zvonkine, An algebra of power series arising in the intersection theory of moduli spaces of curves and in the enumeration of ramified coverings of the sphere, arXiv:0403092v2 [math.AG]
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
|
|
|
FORMULA
| Equals n*A000435(n).
E.g.f: (LambertW(-x)/(1+LambertW(-x)))^2 - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2001
a(n)=sum(k=1, n-1, binomial(n, k)*(n-k)^(n-k)*k^k) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 22 2003
|
|
|
MAPLE
| A001864 := proc(n) local k; add(n!*n^k/k!, k=0..n-2); end;
|
|
|
MATHEMATICA
| Table[Sum[Binomial[n, k](n-k)^(n-k) k^k, {k, 1, n-1}], {n, 20}] (* From Harvey P. Dale, Oct 10 2011 *)
|
|
|
PROG
| (PARI) a(n)=sum(k=1, n-1, binomial(n, k)*(n-k)^(n-k)*k^k)
|
|
|
CROSSREFS
| Cf. A000435, A001863.
Sequence in context: A135389 A065513 A119491 * A099045 A181174 A081065
Adjacent sequences: A001861 A001862 A001863 * A001865 A001866 A001867
|
|
|
KEYWORD
| nonn,easy,nice,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
