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A029767
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(n-1)!*(2^n-1).
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6
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0, 1, 3, 14, 90, 744, 7560, 91440, 1285200, 20603520, 371226240, 7428153600, 163459296000, 3923502105600, 102017281766400, 2856571067750400, 85698439706880000, 2742370993410048000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Labeled octupi with n nodes.
a(n) is the number of connected endofunctions on n points such that every nonrecurrent element has at most one preimage and every recurrent element has at most two preimages. - Geoffrey Critzer, Dec 07 2011
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REFERENCES
| F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, pp. 12, 55, 409.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.5.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 498
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 777
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FORMULA
| (n-1)!*(2^n-1). E.g.f.: log(1-x)-log(1-2*x).
In Maple notation, representation as an infinite sum: a(n)=sum((n+k)!/((k+1)!*2^k), k=0..infinity)/2, n=1, 2... Representation as n-th moment of a positive function on a positive half-axis: a(n)=int(x^n*1/2*exp(-x)/x*(2*exp(1/2*x)-2), x=0..infinity), n=1, 2... - Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 15 2002
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MAPLE
| with(combinat):seq((stirling1(j+1, 1)*(stirling2(j+2, 2))*(-1)^j), j=-1..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 30 2007
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MATHEMATICA
| a=x/(1-x); Range[0, 20]! CoefficientList[Series[Log[1/(1-a)], {x, 0, 20}], x] (* Geoffrey Critzer, Dec 07 2011 *)
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CROSSREFS
| Cf. A001865.
Sequence in context: A088789 A202293 A202294 * A120056 A125788 A183611
Adjacent sequences: A029764 A029765 A029766 * A029768 A029769 A029770
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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