cp's OEIS Frontend

A138781 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).

%I A138781 #2 Mar 30 2012 17:36:16
%S A138781 1,2,3,2,3,16,32,16,3,4,46,200,305,200,46,4,5,100,770,2380,3472,2380,
%T A138781 770,100,5,6,185,2230,11600,30240,41244,30240,11600,2230,185,6,7,308,
%U A138781 5362,42140,172795,393008,515332,393008,172795,42140,5362,308,7
%N A138781 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 A138781 Row n has 2n-1 terms.
%C A138781 Sum of entries in row n is A097184(n-1).
%D A138781 A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189.
%F A138781 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 A138781 Triangle starts:
%e A138781 1;
%e A138781 2,3,2;
%e A138781 3,16,32,16,3;
%e A138781 4,46,200,305,200,46,4
%p A138781 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 A138781 Cf. A097184.
%K A138781 nonn,tabf
%O A138781 1,2
%A A138781 _Emeric Deutsch_, May 11 2008