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%I #16 Feb 02 2024 17:52:52
%S 1,2,4,32,608,23296,1709056,238880768,64396439552,33943701028864,
%T 35324404321091584,72994114660256448512,300460426062916084563968,
%U 2468021884106048216693211136,40495494119922790159005962469376,1328011048967552376327692463141552128
%N Number of connected labeled graphs with loops.
%H Alois P. Heinz, <a href="/A062740/b062740.txt">Table of n, a(n) for n = 0..80</a>
%F E.g.f.: 1+log( Sum_{n >= 0} 2^binomial(n+1, 2)*x^n/n! ).
%F E.g.f.: A(2*x) where A(x) is the e.g.f. for A001187. - _Geoffrey Critzer_, Feb 01 2014
%p logtr:= proc(p) local b; b:= proc(n) option remember; if n=0 then 1 else p(n)- add(k *binomial(n, k) *p(n-k) *b(k), k=1..n-1)/n fi end end:
%p a:= logtr(n-> 2^binomial(n+1, 2)):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 01 2014
%t nn=14;g=Sum[2^Binomial[n,2](2x)^n/n!,{n,0,nn}];Range[0,nn]!CoefficientList[Series[Log[g]+1,{x,0,nn}],x] (* _Geoffrey Critzer_, Feb 01 2014 *)
%Y Cf. A006125, A226773.
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, Jul 12 2001