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Search: id:A134956
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| A134956 |
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Number of hyperforests with n labeled vertices: analogue of A134954 when edges of size 1 are allowed (with no two equal edges). |
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+0
5
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| 1, 2, 8, 64, 880, 17984, 495296, 17255424, 728771584, 36208782336, 2069977144320, 133869415030784, 9664049202221056, 770400218809384960, 67219977066339008512, 6372035504466437079040, 652103070162164448952320, 71656927837957783339925504
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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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FORMULA
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Equals 2^n*A134954(n).
a(n) = Sum of n!prod_{k=1}^n\{ frac{ A134958(k)^{c_k} }{ k!^{c_k} 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
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with (combinat): p:= proc(n) option remember; add (stirling2 (n-1, i) *n^(i-1), i=0..n-1) end: g:= proc(n) option remember; p(n) +add (binomial (n-1, k-1) *p(k) *g(n-k), k=1..n-1) end: a:= n-> `if` (n=0, 1, 2^n * g(n)): seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 07 2008]
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CROSSREFS
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Cf. A134958. [From W. Bomfim (webonfim(AT)bol.com.br), Sep 25 2008]
Adjacent sequences: A134953 A134954 A134955 this_sequence A134957 A134958 A134959
Sequence in context: A092934 A139679 A005640 this_sequence A011803 A007625 A085658
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KEYWORD
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nonn
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AUTHOR
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D. E. Knuth, Jan 26 2008
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