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%I #6 Sep 20 2024 03:20:22
%S 1,-2,1,4,-8,1,-8,36,-12,1,16,-128,80,-16,1,-32,400,-400,140,-20,1,64,
%T -1152,1680,-896,216,-24,1,-128,3136,-6272,4704,-1680,308,-28,1,256,
%U -8192,21504,-21504,10560,-2816
%N A scaled version of the coefficient array for orthogonal polynomials defined by C(2n,n).
%C Inverse is A128413.
%F Number triangle T(n,k)=A128411(n,k)/(2^(k-1)+0^k/2).
%F Column k has g.f. if(k=0,1/(1+2*x),(1-2*x)*x^k/(1+2*x)^(2*k+1)).
%e Triangle begins:
%e 1,
%e -2, 1,
%e 4, -8, 1,
%e -8, 36, -12, 1,
%e 16, -128, 80, -16, 1,
%e -32, 400, -400, 140, -20, 1,
%e 64, -1152, 1680, -896, 216, -24, 1,
%e -128, 3136, -6272, 4704, -1680, 308, -28, 1,
%e 256, -8192, 21504, -21504, 10560, -2816, 416, -32, 1,
%e -512, 20736, -69120, 88704, -57024, 20592, -4368, 540, -36, 1,
%e 1024, -51200, 211200, -337920, 274560, -128128, 36400, -6400, 680, -40, 1
%K easy,sign,tabl
%O 0,2
%A _Paul Barry_, Mar 02 2007