The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 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 Cf. A001187, A218378, A182124. Sequence in context: A198602 A214338 A084275 * A258488 A297052 A238566 Adjacent sequences:  A218374 A218375 A218376 * A218378 A218379 A218380 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)