%I A144208
%S A144208 1,1,1,2,17,221,3261,54801,1049235,22695027,548904831,14701691121,
%T A144208 432342705351,13856514927207,480891887472585,17971038945463101,
%U A144208 719613541474095591,30743125693699501431,1395902175504288127695
%N A144208 Number of simple graphs on n labeled nodes, where each maximally connected 
               subgraph consists of a single node or has a unique cycle of length 
               3; also row sums of A144207.
%F A144208 a(n) = Sum_{k=0..n} A144207(n,k).
%e A144208 a(3) = 2, because there are 2 simple graphs on 3 labeled nodes, where 
               each maximally connected subgraph consists of a single node or has 
               a unique cycle of length 3:
%e A144208 .1.2. .1-2.
%e A144208 ..... .|/..
%e A144208 .3... .3...
%p A144208 T:= proc(n,k) option remember; if k=0 then 1 elif k<0 or n<k then 0 elif 
               k=n then binomial (n-1,2) *n^(n-3) else T(n-1,k) +add (binomial (n-1,
               j) * T(j+1,j+1) *T(n-1-j,k-j-1), j=2..k-1) fi end: a:= n-> add (T(n,
               k), k=0..n): seq (a(n), n=0..23);
%Y A144208 Row sums of triangle A144207. Cf. A053507, A007318.
%Y A144208 Sequence in context: A058010 A126752 A004029 this_sequence A058239 A006227 
               A036082
%Y A144208 Adjacent sequences: A144205 A144206 A144207 this_sequence A144209 A144210 
               A144211
%K A144208 nonn
%O A144208 0,4
%A A144208 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 14 2008