login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

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

Table of n, a(n) for n=0..15.

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

Adjacent sequences:  A182121 A182122 A182123 * A182125 A182126 A182127

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 11:20 EST 2021. Contains 340254 sequences. (Running on oeis4.)