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 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 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

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