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A134955
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Number of "hyperforests" on n unlabeled nodes, i.e. hypergraphs that have no cycles, assuming that each edge contains at least two vertices.
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6
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1, 1, 2, 4, 9, 20, 50, 128, 351, 1009, 3035, 9464, 30479, 100712, 340072, 1169296, 4082243, 14438577, 51643698, 186530851, 679530937, 2494433346, 9219028889, 34280914106, 128179985474, 481694091291, 1818516190252, 6894350122452
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| D. E. Knuth: The Art of Computer Programming, Volume 4, Generating All Combinations and Partitions Fascicle 3, Section 7.2.1.4. Generating all partitions. Page 38, Algorithm H. [From W. Bomfim (webonfim(AT)bol.com.br), Sep 25 2008]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
N. J. A. Sloane, Transforms
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FORMULA
| Euler transform of A035053. - N. J. A. Sloane , Jan 30 2008
a(n) = Sum of prod_{k=1}^n\,{A035053(k) + c_k -1 /choose c_k} over all the partitions of n, c_1 + 2c_2 + ... + nc_n; c_1, c_2, ..., c_n >= 0. [From W. Bomfim (webonfim(AT)bol.com.br), Sep 25 2008]
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MAPLE
| 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): aa:= proc(n) option remember; B(n)+C(n) -add (B(k)*C(n-k), k=0..n) end: a:= etr(aa): seq (a(n), n=0..27); # Alois P. Heinz, Sep 09 2008
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CROSSREFS
| Cf. A035053 (hypertrees), A134954 (labeled case).
Sequence in context: A032289 A006648 A128496 * A171887 A027881 A002861
Adjacent sequences: A134952 A134953 A134954 * A134956 A134957 A134958
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KEYWORD
| nonn
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AUTHOR
| D. E. Knuth, Jan 26 2008
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