Search: id:A120733
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%I A120733
%S A120733 1,1,5,33,281,2961,37277,546193,9132865,171634161,3581539973,82171451025,
%T A120733 2055919433081,55710251353953,1625385528173693,50800411296363617,1693351638586070209,
%U A120733 59966271207156833313,2248276994650395873861,88969158875611127548481
%N A120733 Number of matrices with nonnegative integer entries and without zero 
               rows or columns such that sum of all entries is equal to n.
%C A120733 Partial sums give A007322.
%C A120733 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
%H A120733 G. Duchamp, F. Hivert and J.-Y. Thibon, <a href="http://arXiv.org/abs/
               math.CO/0105065">Noncommutative symmetric functions VI: Free quasi-symmetric 
               functions and related algebras</a>,Internat. J. Alg. Comp. 12 (2002), 
               671-717
%F A120733 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.
%F A120733 a(n) = Sum_{r>=0,s>=0} binomial(r*s+n-1,n)/2^(r+s+2).
%F A120733 G.f.: Sum_{n>=0} 1/(2-(1-x)^(-n))/2^(n+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 30 2006
%p A120733 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
%Y A120733 Cf. A101370, A007322, A120732.
%Y A120733 Sequence in context: A135075 A049377 A129890 this_sequence A144792 A001828 
               A084845
%Y A120733 Adjacent sequences: A120730 A120731 A120732 this_sequence A120734 A120735 
               A120736
%K A120733 nonn
%O A120733 0,3
%A A120733 Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 18 2006, Aug 21 2006
%E A120733 More terms from N. J. A. Sloane (njas(AT)research.att.com), Jan 14 2009

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