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Search: id:A073225
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| 1, 1, 2, 5, 11, 27, 65, 164, 417, 1068, 2756, 7148, 18614, 48639, 127464, 334865, 881658, 2325751, 6145597, 16263867, 43099805, 114356612, 303761261, 807692035, 2149632062, 5726042116, 15264691108, 40722913455, 108713644517
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OFFSET
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0,3
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COMMENT
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The van der Waerden conjecture, now a theorem thanks to Egorycev, states that the permanent of any n X n doubly stochastic matrix is >= n!/n^n, with equality iff the matrix has all entries equal to 1/n.
Therefore the reciprocal of the permanent of any n X n doubly stochastic matrix is bounded from above by n^n/n! and this sequence.
n^n/n! = A001142(n)/A001142(n-1), where A001142(n) is product{k=0 to n} C(n,k) (where C() is a binomial coefficient). - Leroy Quet, May 01 2004
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REFERENCES
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G. P. Egorycev, Solution of the van der Waerden problem for permanents (Russian), Preprint IFSO-13 M. Akad. Nauk SSSR Sibirsk. Otdel., Inst. Fiz., Krasnoyarsk, 1980. 12 pp. Math. Rev. 82e:15006.
J. H. van Lint, R. M. Wilson, A Course in Combinatorics, Cambridge Univ. Press, 1992. p. 86.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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PROGRAM
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(PARI) a(n)=ceil(n^n/n!)
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CROSSREFS
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Cf. A055775, A094082.
Sequence in context: A067922 A095975 A006652 this_sequence A027087 A055227 A124016
Adjacent sequences: A073222 A073223 A073224 this_sequence A073226 A073227 A073228
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jul 22, 2002
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