|
| |
|
|
A002031
|
|
Number of labeled connected digraphs on n nodes where every node has indegree 0 or outdegree 0 and no isolated nodes.
(Formerly M1707 N0676)
|
|
16
|
|
|
|
2, 6, 38, 390, 6062, 134526, 4172198, 178449270, 10508108222, 853219059726, 95965963939958, 15015789392011590, 3282145108526132942, 1005193051984479922206, 432437051675617901246918, 261774334771663762228012950, 223306437526333657726283273822
(list;
graph;
refs;
listen;
history;
text;
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.
In- or outdegree zero implies loops are not admitted. Multi-arcs are not admitted. - R. J. Mathar, Nov 18 2023
|
|
|
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
|
|
|
|
FORMULA
|
E.g.f.: log(Sum(exp((2^n-2)*x)*x^n/n!, n=0..infinity)). - Vladeta Jovovic, 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
|
terms = 17; s = Log[Sum[Exp[(2^n - 2)*x]*(x^n/n!), {n, 0, terms+2}]] + O[x]^(terms+2); Drop[CoefficientList[s, x]*Range[0, terms+1]!, 2] (* Jean-François Alcover, Nov 08 2011, after Vladeta Jovovic, updated Jan 12 2018 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
