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Search: id:A035053
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| A035053 |
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Number of connected graphs on n unlabeled nodes where every block is a complete graph. |
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+0
9
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| 1, 1, 1, 2, 4, 9, 22, 59, 165, 496, 1540, 4960, 16390, 55408, 190572, 665699, 2354932, 8424025, 30424768, 110823984, 406734060, 1502876903, 5586976572, 20884546416, 78460794158, 296124542120, 1122346648913, 4270387848473
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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.
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REFERENCES
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F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 71, (3.4.14).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
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FORMULA
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G.f.: A(x)=1+(C(x)-1)*(1-B(x)). B: G.f. for A007563. C: G.f. for A035052.
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MAPLE
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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]
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CROSSREFS
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Cf. A007549, A007563, A030019, A035051, A035052, A134957, A134959.
Sequence in context: A121953 A024427 A092920 this_sequence A000571 A077003 A046917
Adjacent sequences: A035050 A035051 A035052 this_sequence A035054 A035055 A035056
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Oct 15 1998.
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