Search: id:A035053
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%I A035053
%S A035053 1,1,1,2,4,9,22,59,165,496,1540,4960,16390,55408,190572,665699,2354932,
%T A035053 8424025,30424768,110823984,406734060,1502876903,5586976572,
%U A035053 20884546416,78460794158,296124542120,1122346648913,4270387848473
%N A035053 Number of connected graphs on n unlabeled nodes where every block is 
               a complete graph.
%C A035053 Equivalently, this is the number of "hypertrees" on n unlabeled nodes, 
               i.e. connected hypergraphs that have no cycles, assuming that each 
               edge contains at least two vertices. - D. E. Knuth, Jan 26 2008. 
               See A134955 for hyperforests.
%D A035053 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 71, (3.4.14).
%H A035053 T. D. Noe, <a href="b035053.txt">Table of n, a(n) for n=0..200</a>
%F A035053 G.f.: A(x)=1+(C(x)-1)*(1-B(x)). B: G.f. for A007563. C: G.f. for A035052.
%p A035053 with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; 
               `if`(n=0,1, add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n) 
               end end: b:= etr(B): c:= etr(b): B:= n-> if n=0 then 0 else c(n-1) 
               fi: C:= etr (B): a:= n-> B(n)+C(n) -add (B(k)*C(n-k), k=0..n): seq 
               (a(n), n=0..27); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Sep 09 2008]
%Y A035053 Cf. A007549, A007563, A030019, A035051, A035052, A134957, A134959.
%Y A035053 Sequence in context: A121953 A024427 A092920 this_sequence A000571 A077003 
               A046917
%Y A035053 Adjacent sequences: A035050 A035051 A035052 this_sequence A035054 A035055 
               A035056
%K A035053 nonn,easy,nice
%O A035053 0,4
%A A035053 Christian G. Bower (bowerc(AT)usa.net), Oct 15 1998.

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