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A048291
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Number of {0,1} n X n matrices with no zero rows or columns.
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12
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1, 1, 7, 265, 41503, 24997921, 57366997447, 505874809287625, 17343602252913832063, 2334958727565749108488321, 1243237913592275536716800402887, 2630119877024657776969635243647463625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of relations on n labeled points such that for every point x there exists y and z such that xRy and zRx.
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REFERENCES
| Posting to sci.math.research from bdm(AT)cs.anu.edu.au (Brendan McKay), Jun 14 1999.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..32
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FORMULA
| Sum over s=0..n of binomial(n, s)*(-1)^s*2^((n-s)*n)*(1-2^(-n+s))^n.
E.g.f.: Sum((2^n-1)^n*exp((1-2^n)*x)*x^n/n!,n=0..infinity). a(n) = Sum(Sum((-1)^(i+j)*binomial(n,i)*binomial(n,j)*2^(i*j),j = 0 .. n),i = 0 .. n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 23 2008
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(n, k)*(-1)^k*(2^(n-k)-1)^n)
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CROSSREFS
| Cf. A054976.
Cf. A055601, A055599, A104601, A086193, A086206.
Sequence in context: A130741 A003385 A129423 * A015089 A179565 A069449
Adjacent sequences: A048288 A048289 A048290 * A048292 A048293 A048294
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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