Search: id:A045912
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%I A045912
%S A045912 1,1,1,1,3,1,1,9,9,1,1,29,72,29,1,1,99,626,626,99,1,1,351,6084,
%T A045912 13869,6084,351,1,1,1275,64974,347020,347020,64974,1275,1,1,4707,
%U A045912 744193,9952274,21537270,9952274,744193,4707,1,1,17577,8965323
%N A045912 Triangle of coefficients of characteristic polynomial of negative Pascal 
               matrix with (i,j)-th entry -C(i+j-2,i-1).
%C A045912 Sum of k-th row is A006366(n). Columns give A006134, A006135, A006136.
%D A045912 W. F. Lunnon "The Pascal matrix", Fib. Quart. vol. 15 (1977) pp. 201-204.
%H A045912 P. Di Francesco, P. Zinn-Justin and J.-B. Zuber, <a href="http://arXiv.org/
               abs/math-ph/0410002">Determinant formulae for some tiling problems...</
               a>
%e A045912 1; 1,1; 1,3,1; 1,9,9,1; 1,29,72,29,1; ...
%o A045912 (PARI) T(n,k)=if(n<0,0,(-1)^(n+k)*polcoeff(charpoly(matrix(n,n,i,j,binomial(i+j-2,
               i-1))),k))
%o A045912 (PARI) T(n,k)=if(n<0,0,polcoeff(charpoly(-matrix(n,n,i,j,binomial(i+j-2,
               i-1))),k))
%Y A045912 Sequence in context: A152655 A144493 A118180 this_sequence A158695 A106268 
               A060543
%Y A045912 Adjacent sequences: A045909 A045910 A045911 this_sequence A045913 A045914 
               A045915
%K A045912 nonn
%O A045912 0,5
%A A045912 Fred Lunnon (fred(AT)csa5.cs.may.ie)

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