|
%I #12 Mar 19 2018 04:14:30
%S 1,2,4,26,296,5904,225576,16673252,2410709536,686706538432,
%T 386940976402960,432315602878003448,959210666655240937120,
%U 4231214210938514819918144,37138134131400012001269996000,649036769087148274525770997003248,22596872562588017123584720776207222528
%N The number of simple labeled graphs on n nodes with no components of size 1 or 2.
%H Vincenzo Librandi, <a href="/A182146/b182146.txt">Table of n, a(n) for n = 1..80</a>
%F E.g.f.: G(x)-G(x)/(exp(x)*exp(x^2/2)) where G(x) is the e.g.f. for A006125.
%e a(4) = 26 because we have: * * * *; * * *-* times 6 labelings; *-*-* * times 12 labelings; *-* *-* times 3 labelings; and the complete graph on three nodes union with an isolated node which has 4 labelings. 1+6+12+3+4 = 26.
%t nn = 17; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; Drop[Range[0, nn]! CoefficientList[Series[g - g/(Exp[x] Exp[x^2/2]), {x, 0, nn}], x], 1]
%K nonn
%O 1,2
%A _Geoffrey Critzer_, Apr 14 2012
|
