The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218377 Number of simple labeled graphs on 2n nodes with all even size components. 1
1, 1, 41, 27289, 252354929, 34508040597841, 73356878424474928601, 2471655487735117774297253929, 1328579254939122192980041623517564769, 11416413723707413064765254593047001003783424801, 2169118832800743175599952429700612077287847317513 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
These are precisely the graphs G in which there exists a spanning subgraph F of G such that every vertex in F has odd degree. The number of such subgraphs in any such graph G is 2^(m-n+c) where m,n,c is the number of edges, vertices, and components of G respectively. - Geoffrey Critzer, Feb 23 2020
LINKS
FORMULA
E.g.f. for the sequence with interpolated 0's is: exp( ( A(x) + A(-x) - 2 )/2) where A(x) is the e.g.f. for A001187.
EXAMPLE
a(2) = 41 because (on 4 labeled nodes) we have 38 connected graphs and 3 in the isometry class o-o o-o.
MATHEMATICA
nn=20; a=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; c=Range[0, nn]! CoefficientList[Series[ Log[a]+1, {x, 0, nn}], x]; cx= Sum[c[[i]]x^(i-1)/(i-1)!, {i, 1, nn, 2}]; Select[Range[0, nn]! CoefficientList[Series[Exp[cx-1], {x, 0, nn}], x], #>0&]
CROSSREFS
Sequence in context: A198602 A214338 A084275 * A258488 A297052 A238566
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 27 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 13:18 EDT 2024. Contains 372773 sequences. (Running on oeis4.)