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 A182117 The number of simple unlabelled graphs whose connected components have distinct sizes (no two connected components have the same number of nodes). 1
 1, 1, 1, 3, 8, 29, 141, 1004, 12157, 273566, 11992403, 1018721807, 165079148151, 50501012085899, 29053990553658291, 31426435466752989418, 64000986650206723016967, 245935832726996458741850870, 1787577661144566941500116028526, 24637809007189108944263048282845188 (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.: prod(n>=1, 1 + A001349(n)*x^n ) where A001349 is the number of connected graphs. MATHEMATICA nn = 19; c = (A000088 = Table[NumberOfGraphs[n], {n, 0, nn}]; f[x_] = 1 - Product[1/(1 - x^k)^a[k], {k, 1, nn}]; a[0] = a[1] = a[2] = 1; coes = CoefficientList[Series[f[x], {x, 0, nn}], x]; sol = First[Solve[Thread[Rest[coes + A000088] == 0]]]; Table[a[n], {n, 0, nn}] /. sol); p = Product[1 + c[[n + 1]] x^n, {n, 1, nn}]; CoefficientList[ Series[p, {x, 0, nn}], x] (* The Mma code for c in the above is given by Jean-François Alcover in A001349. *) CROSSREFS Cf. A207828. Sequence in context: A192744 A130470 A275166 * A207828 A208678 A162054 Adjacent sequences: A182114 A182115 A182116 * A182118 A182119 A182120 KEYWORD nonn AUTHOR Geoffrey Critzer, Apr 12 2012 STATUS approved

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)