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A132431
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For n>0, let B_n be the subsemigroup of the full transformation monoid on the n-set [n] generated by the following functions: Let x be a certain element in [n]. Now the generators of B are those functions which map either x to any distinct element y in [n] leaving all the other elements fixed, or y to x leaving all the other elements fixed. Then a(n) = number of elements in B_n.
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1
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0, 2, 9, 88, 1385, 24336, 466753, 9906688, 233522577, 6093136000, 174912502721, 5487091383456, 186891076515481, 6870622015481056, 271195480556337345, 11440127985767481856, 513639921634424850977, 24455974520989478444544, 1230835712617872016215265
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OFFSET
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1,2
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COMMENTS
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Let b(n)=n^n be the cardinality of the full transformation monoid. The sequence of quotients a(n)/b(n) converges to 1-1/e.
a(n) = A060226(n) - A062119(n) + A002378(n-1). - Reinhard Zumkeller, Aug 27 2012
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REFERENCES
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S. Bogner, Eine Praesentation der Halbgruppe der singularen zyklisch-monotonen Abbildungen UND eine von Idempotenten erzeugte Unterhalbgruppe von T_n (Studienarbeit in Informatik, Advisor: Klaus Leeb), Friedrich-Alexander-Universitaet Erlangen-Nuernberg, 2007.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..250
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FORMULA
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a(n) = n^n - n(n-1)^(n-1) - (n-1)n! + n(n-1). a(n) = n*(n-1) + sum_{k=1..n-2} k*Stirling2(n-1,k)*k!*C(n,k).
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PROG
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(Haskell)
a132431 n = a060226 n - a062119 n + a002378 (n - 1)
-- Reinhard Zumkeller, Aug 27 2012
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CROSSREFS
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Cf. A000312, A060226.
Sequence in context: A037172 A106163 A135747 * A001192 A006120 A012941
Adjacent sequences: A132428 A132429 A132430 * A132432 A132433 A132434
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KEYWORD
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nice,nonn
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AUTHOR
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Simon Bogner (sisibogn(AT)stud.informatik.uni-erlangen.de), Nov 20 2007
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STATUS
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approved
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