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Search: id:A120733
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| A120733 |
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Number of matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n. |
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+0
2
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| 1, 1, 5, 33, 281, 2961, 37277, 546193, 9132865, 171634161, 3581539973, 82171451025, 2055919433081, 55710251353953, 1625385528173693, 50800411296363617, 1693351638586070209, 59966271207156833313, 2248276994650395873861, 88969158875611127548481
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Partial sums give A007322.
Dimensions of the graded components of the Hopf algebra MQSym (Matrix quasi-symmetric funcions). - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 23 2006
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LINKS
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G. Duchamp, F. Hivert and J.-Y. Thibon, Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras,Internat. J. Alg. Comp. 12 (2002), 671-717
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FORMULA
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a(n) = (1/n!)*Sum_{k=1..n} (-1)^(n-k)*Stirling1(n,k)*A000670(k)^2. G.f.: Sum_{m>=0,n>=0} Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*((1-x)^(-j)-1)^m.
a(n) = Sum_{r>=0,s>=0} binomial(r*s+n-1,n)/2^(r+s+2).
G.f.: Sum_{n>=0} 1/(2-(1-x)^(-n))/2^(n+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 30 2006
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MAPLE
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t1:= M-> add( add( add( (-1)^(n-j)*binomial(n, j)*((1-x)^(-j)-1)^m, j=0..n), n=0..M), m=0..M); t1(20): seriestolist(%); # from N. J. A. Sloane (njas(AT)research.att.com), Jan 14 2009
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CROSSREFS
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Cf. A101370, A007322, A120732.
Sequence in context: A135075 A049377 A129890 this_sequence A144792 A001828 A084845
Adjacent sequences: A120730 A120731 A120732 this_sequence A120734 A120735 A120736
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 18 2006, Aug 21 2006
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EXTENSIONS
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More terms from N. J. A. Sloane (njas(AT)research.att.com), Jan 14 2009
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