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A054913 Number of labeled connected graphs with n nodes such that complement is also connected. 1
1, 0, 0, 12, 432, 20640, 1635360, 234661728, 63873105408, 33808605100800, 35254518078942720, 72922216118695037952, 300312950395670884227072, 2467417543490126920783534080, 40490542668157619621325008117760, 1327929920886650529112870913410510848 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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.

FORMULA

a(n) = 2*A001187(n) - A006125(n).

MAPLE

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

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A123778 A129006 A067429 * A221955 A070285 A241593

Adjacent sequences:  A054910 A054911 A054912 * A054914 A054915 A054916

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 23 2000

EXTENSIONS

More terms from Vladeta Jovovic, Jul 19 2000

STATUS

approved

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Last modified June 6 16:57 EDT 2020. Contains 334829 sequences. (Running on oeis4.)