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%I #2 Mar 30 2012 17:36:16
%S 1,2,3,2,3,16,32,16,3,4,46,200,305,200,46,4,5,100,770,2380,3472,2380,
%T 770,100,5,6,185,2230,11600,30240,41244,30240,11600,2230,185,6,7,308,
%U 5362,42140,172795,393008,515332,393008,172795,42140,5362,308,7
%N Triangle read by rows: coefficients of polynomials arising in the spontaneous magnetization of the anisotropic square lattice Ising model (see pp. 174-5 of the Guttmann reference).
%C Row n has 2n-1 terms.
%C Sum of entries in row n is A097184(n-1).
%D A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189.
%F The row generating polynomial P[n,y] of row n is defined by 1-M(x,y)=2*y*Sum(P[n,y]/(1-y)^(2n)*x^n, n=1..infinity), where M(x,y)=(1-16xy/[(1-x)^2*(1-y)^2])^(1/8).
%e Triangle starts:
%e 1;
%e 2,3,2;
%e 3,16,32,16,3;
%e 4,46,200,305,200,46,4
%p M:=(1-16*x*y/((1-x)^2*(1-y)^2))^(1/8): oneminusM:=simplify(series(1-M,x=0, 10)): for n to 7 do P[n]:=sort((1/2)*(y-1)^(2*n)*coeff(oneminusM,x,n)/y) end do: for n to 7 do seq(coeff(P[n],y,k),k=0..2*n-2) end do; # yields sequence in triangular form
%Y Cf. A097184.
%K nonn,tabf
%O 1,2
%A _Emeric Deutsch_, May 11 2008
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