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Search: id:A034841
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| 1, 6, 1680, 63063000, 623360743125120, 2670177736637149247308800, 7363615666157189603982585462030336000, 18165723931630806756964027928179555634194028454000000
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OFFSET
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1,2
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COMMENT
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The number of arrangements of 1,2,..,n*n in an n*n matrix such that each row is increasing. - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 12 2001
a(n)== 0 mod (n!) In fact (n^2)! == 0 mod (n!)^n by elementary combinatorics, a better result is (n^2)! == 0 ((mod(n!)^(n+1)). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 13 2005
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FORMULA
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Using a higher order version of Stirling's formula (the "standard" formula appears in A000142) we have the asymptotic expression: a(n) ~ sqrt(2*pi) * e^(-1/12) * n^(n^2 - n/2 + 1) / (2*pi)^(n/2). - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 13 2001
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CROSSREFS
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Cf. A000142, A039622.
Sequence in context: A107252 A131453 A160226 this_sequence A149187 A160301 A024086
Adjacent sequences: A034838 A034839 A034840 this_sequence A034842 A034843 A034844
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu)
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