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A054913
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Number of labeled connected graphs with n nodes such that complement is also connected.
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1
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1, 0, 0, 12, 432, 20640, 1635360, 234661728, 63873105408, 33808605100800, 35254518078942720, 72922216118695037952, 300312950395670884227072, 2467417543490126920783534080, 40490542668157619621325008117760, 1327929920886650529112870913410510848
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OFFSET
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1,4
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..50
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
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FORMULA
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a(n) = 2*A001187(n) - A006125(n).
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MAPLE
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b:= n-> 2^(n*(n-1)/2):
g:= proc(n) option remember; local k; `if`(n=0, 1,
b(n)- add(k*binomial(n, k) *b(n-k)*g(k), k=1..n-1)/n)
end:
a:= n-> 2*g(n)-b(n):
seq (a(n), n=1..20); # Alois P. Heinz, Oct 21 2012
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MATHEMATICA
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nn=20; g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; Drop[Range[0, nn]!CoefficientList[Series[2(Log[g]+1)-g, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Oct 21 2012 *)
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CROSSREFS
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Sequence in context: A123778 A129006 A067429 * A221955 A070285 A041617
Adjacent sequences: A054910 A054911 A054912 * A054914 A054915 A054916
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane, May 23 2000
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EXTENSIONS
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More terms from Vladeta Jovovic, Jul 19 2000
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STATUS
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approved
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