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A000220 Number of asymmetric trees with n nodes (also called identity trees).
(Formerly M2583 N1022)
10
1, 0, 0, 0, 0, 0, 1, 1, 3, 6, 15, 29, 67, 139, 310, 667, 1480, 3244, 7241, 16104, 36192, 81435, 184452, 418870, 955860, 2187664, 5025990, 11580130, 26765230, 62027433, 144133676, 335731381, 783859852, 1834104934, 4300433063, 10102854473 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 330.

S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 301 and 562.

F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 232.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 66, Eq. (3.3.22).

F. Harary, R. W. Robinson and A. J. Schwenk, Twenty-step algorithm for determining the asymptotic number of trees of various species, J. Austral. Math. Soc., Series A, 20 (1975), 483-503. Errata: Vol. A 41 (1986), p. 325.

D. E. Knuth, Fundamental Algorithms, 3d Ed. 1997, pp. 386-88 describes methodology for generating similar sequence rapidly.

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

A. J. Schwenk, personal communication.

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).

LINKS

T. D. Noe, Table of n, a(n) for n=1..200

E. Friedman, Illustration of initial terms

Index entries for sequences related to trees

FORMULA

G.f.: A(x)-A^2(x)/2-A(x^2)/2, where A(x) is g.f. for A004111.

a(n) ~ c * d^n / n^(5/2), where d = A246169 = 2.51754035263200389079535..., c = 0.29938828746578432274375484519722721162... . - Vaclav Kotesovec, Aug 25 2014

MATHEMATICA

s[ n_, k_ ] := s[ n, k ]=a[ n+1-k ]+If[ n<2k, 0, -s[ n-k, k ] ]; a[ 1 ]=1; a[ n_ ] := a[ n ]=Sum[ a[ i ]s[ n-1, i ]i, {i, 1, n-1} ]/(n-1); Table[ a[ i ]-Sum[ a[ j ]a[ i-j ], {j, 1, i/2} ]+If[ OddQ[ i ], 0, a[ i/2 ](a[ i/2 ]-1)/2 ], {i, 1, 50} ] (from Robert A. Russell)

CROSSREFS

Cf. A000055, A000081.

Cf. A246169, A004111, A035056.

Sequence in context: A066708 A034464 A116696 * A244705 A092641 A077449

Adjacent sequences:  A000217 A000218 A000219 * A000221 A000222 A000223

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 14 21:54 EDT 2014. Contains 246769 sequences.