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A134954
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Number of "hyperforests" on n labeled nodes, i.e. hypergraphs that have no cycles, assuming that each edge contains at least two vertices.
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4
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1, 1, 2, 8, 55, 562, 7739, 134808, 2846764, 70720278, 2021462055, 65365925308, 2359387012261, 94042995460130, 4102781803365418, 194459091322828280, 9950303194613104995, 546698973373090998382, 32101070021048906407183
(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
| Alois P. Heinz, Table of n, a(n) for n = 0..135
N. J. A. Sloane, Transforms
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FORMULA
| Exponential transform of A030019. - N. J. A. Sloane, Jan 30 2008
a(n) = Sum of n!prod_{k=1}^n\{ frac{ A030019(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
| with (combinat): b:= proc(n) option remember; add (stirling2 (n-1, i) *n^(i-1), i=0..n-1) end: B:= proc(n) x-> add (b(k) *x^k/k!, k=0..n) end: a:= n->coeff (series (exp (B(n)(x)), x, n+1), x, n) *n!: seq (a(n), n=0..30); # Alois P. Heinz, Sep 09 2008
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CROSSREFS
| Cf. A030019 (hypertrees), A134955 (unlabeled case), A134956.
Sequence in context: A005440 A183282 A139016 * A087422 A081667 A117496
Adjacent sequences: A134951 A134952 A134953 * A134955 A134956 A134957
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KEYWORD
| nonn
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AUTHOR
| D. E. Knuth, Jan 26 2008
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