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A207828 The number of unlabelled simple graphs with n nodes such that no two connected components are identical. 3
1, 1, 1, 3, 8, 29, 142, 1005, 12173, 273582, 11992634, 1018722089, 165079154766, 50501012094102, 29053990554043728, 31426435466753662607, 64000986650206797417763, 245935832726996459827917035, 1787577661144566941699523416191, 24637809007189108944313598892070582 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 7 10:14 EST 2021. Contains 341869 sequences. (Running on oeis4.)