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Column 1 of triangle A104030, which is the matrix inverse of the triangle of pairwise sums of trinomial coefficients.
1

%I #5 Jan 25 2013 19:01:52

%S 1,-5,32,-299,4015,-74080,1801537,-55855829,2150565968,-100668835739,

%T 5630336915071,-370807060847872,28403381397111649,

%U -2503741873703550533,251652633457563092096,-28608467296650576313259,3652291148549164761101551,-520296573821474451201241696

%N Column 1 of triangle A104030, which is the matrix inverse of the triangle of pairwise sums of trinomial coefficients.

%C Column 0 of triangle A104030 forms signed Hammersley's polynomial p_n(1) (A006846), offset 1.

%o (PARI) {a(n)=if(n<0,0,((matrix(n+2,n+2,m,j,if(m>=j, polcoeff((1+x+x^2)^(m-1)+O(x^(2*j)),2*j-2)+ polcoeff((1+x+x^2)^(m-1)+O(x^(2*j)),2*j-1))))^-1)[n+2,2])}

%Y Cf. A104030.

%K sign

%O 0,2

%A _Paul D. Hanna_, Feb 26 2005