A182124 The number of simple labeled graphs on n nodes such that no two connected components have the same number of nodes.

1, 1, 1, 7, 54, 958, 31882, 2077782, 267554288, 68648260400, 35172685780656, 36025101106326704, 73784683234911510496, 302228664484725680174432, 2475873389968026270223227808, 40564787539851948459971794384480

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