A207828 The number of unlabelled simple graphs with n nodes such that no two connected components are identical.

1, 1, 1, 3, 8, 29, 142, 1005, 12173, 273582, 11992634, 1018722089, 165079154766, 50501012094102, 29053990554043728, 31426435466753662607, 64000986650206797417763, 245935832726996459827917035, 1787577661144566941699523416191, 24637809007189108944313598892070582

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

O.g.f.: Product_{n >=1} (1+x^n)^A001349(n) where A001349 is the number of connected graphs.

Example

a(4)=8 because there are eleven graphs with 4 nodes but three have (at least two) components that are identical:   * * * * ,  *-* *-* , * * *-*

Mathematica

nn=19; a={1, 1, 2, 6, 21, 112, 853, 11117, 261080, 11716571, 1006700565, 164059830476, 50335907869219, 29003487462848061, 31397381142761241960, 63969560113225176176277, 245871831682084026519528568, 1787331725248899088890200576580, 24636021429399867655322650759681644}; CoefficientList[Series[Product[(1+x^i)^a[[i]], {i, 1, nn}], {x, 0, nn}], x]

Crossrefs

Sequence in context: A130470 A275166 A182117 * A208678 A162054 A289486

Adjacent sequences: A207825 A207826 A207827 * A207829 A207830 A207831

Keyword

nonn

Author

Geoffrey Critzer, Feb 20 2012

Status

approved