|
| |
|
|
A002031
|
|
Number of labeled connected digraphs where every node has indegree 0 or outdegree 0 and no isolated nodes.
(Formerly M1707 N0676)
|
|
11
| |
|
|
2, 6, 38, 390, 6062, 134526, 4172198, 178449270, 10508108222, 853219059726, 95965963939958, 15015789392011590, 3282145108526132942, 1005193051984479922206, 432437051675617901246918, 261774334771663762228012950, 223306437526333657726283273822
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,1
|
|
|
COMMENTS
| Also number of labeled connected graphs with 2-colored nodes with no isolated nodes where black nodes are only connected to white nodes and vice versa.
|
|
|
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).
|
|
|
LINKS
| Alois P. Heinz, Table of n, a(n) for n = 2..62
Read, R. C.; Wright, E. M., Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596.
N. J. A. Sloane, Transforms
|
|
|
FORMULA
| Logarithmic transform of A052332.
E.g.f.: ln(Sum(exp((2^n-2)*x)*x^n/n!, n=0..infinity)). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 28 2004
|
|
|
MAPLE
| logtr:= proc(p) local b; b:=proc(n) option remember; local k; if n=0 then 1 else p(n)- add (k *binomial(n, k) *p(n-k) *b(k), k=1..n-1)/n fi end end: digr:= n-> add (binomial(n, k) *(2^k-2)^(n-k), k=0..n): a:= logtr (digr): seq (a(n), n=2..25); # Alois P. Heinz, Sep 14 2008
|
|
|
MATHEMATICA
| max = 18; f[x_] := Sum[ a[n]*(x^n/n!), {n, 0, max}]; coes = CoefficientList[ Series[ f[x] - Log[ Sum[ Exp[ (2^n-2)*x]*(x^n/n!), {n, 0, max}]], {x, 0, max}], x]; Table[a[n], {n, 2, 18}] /. First[ Solve[ Thread[ coes == 0]]] (* From Jean-François Alcover, Nov 08 2011, after Vladeta Jovovic *)
|
|
|
CROSSREFS
| Cf. A001831, A001832, A047863, A052332. Essentially the same as A002027.
Sequence in context: A067106 A032111 A013703 * A184731 A005738 A055704
Adjacent sequences: A002028 A002029 A002030 * A002032 A002033 A002034
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms, formula and new title from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
Corrected by Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 12 2003
|
| |
|
|
