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!)
A182124 The number of simple labeled graphs on n nodes such that no two connected components have the same number of nodes. 2
1, 1, 1, 7, 54, 958, 31882, 2077782, 267554288, 68648260400, 35172685780656, 36025101106326704, 73784683234911510496, 302228664484725680174432, 2475873389968026270223227808, 40564787539851948459971794384480 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
E.g.f.: Product_{n>=1} (1+A001187(n)*x^n/n!) where A001187 is the number of connected labeled graphs.
EXAMPLE
a(4)=54 because there are 64 simple labeled graphs on 4 nodes but 10 of these have (at least) two components of the same size: * * * *; * * *-* times 6 labelings; *-* *-* times 3 labelings.
MATHEMATICA
nn=15; g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; c=Range[0, nn]!CoefficientList[Series[Log[g]+1, {x, 0, nn}], x]; p=Product[1+c[[n+1]]x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[Series[p, {x, 0, nn}], x]
CROSSREFS
Cf. A182117 (the unlabeled case).
Sequence in context: A200140 A298104 A289865 * A303889 A198149 A203878
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 13 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 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)