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%I #2 Mar 30 2012 18:59:27
%S 1,0,1,-1,0,1,0,-4,0,1,5,0,-9,0,1,0,33,0,-16,0,1,-45,0,114,0,-25,0,1,
%T 0,-408,0,290,0,-36,0,1,585,0,-1890,0,615,0,-49,0,1,0,6705,0,-6240,0,
%U 1155,0,-64,0,1,-9945,0,38835,0,-16695,0,1988,0,-81,0,1,0,-137340,0,157395,0
%N Coefficient array of orthogonal polynomials P(n,x)=x*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1,P(1,x)=x.
%C First row is aerated signed version of quartic factorial numbers A007696. Inverse is A178104.
%e Triangle begins
%e 1,
%e 0, 1,
%e -1, 0, 1,
%e 0, -4, 0, 1,
%e 5, 0, -9, 0, 1,
%e 0, 33, 0, -16, 0, 1,
%e -45, 0, 114, 0, -25, 0, 1,
%e 0, -408, 0, 290, 0, -36, 0, 1,
%e 585, 0, -1890, 0, 615, 0, -49, 0, 1
%e Production matrix of inverse is
%e 0, 1,
%e 1, 0, 1,
%e 0, 3, 0, 1,
%e 0, 0, 5, 0, 1,
%e 0, 0, 0, 7, 0, 1,
%e 0, 0, 0, 0, 9, 0, 1,
%e 0, 0, 0, 0, 0, 11, 0, 1,
%e 0, 0, 0, 0, 0, 0, 13, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 15, 0, 1
%K sign,tabl
%O 0,8
%A _Paul Barry_, May 20 2010