

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
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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



