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Generalized Riordan array (1/sqrt(1+4x^2),(1-sqrt(1+4x^2))/(2x)).
1

%I #5 Nov 02 2023 07:25:37

%S 1,0,-1,-2,0,1,0,3,0,-1,6,0,-4,0,1,0,-10,0,5,0,-1,-20,0,15,0,-6,0,1,0,

%T 35,0,-21,0,7,0,-1,70,0,-56,0,28,0,-8,0,1,0,-126,0,84,0,-36,0,9,0,-1,

%U -252,0,210,0,-120,0,45,0,-10,0,1

%N Generalized Riordan array (1/sqrt(1+4x^2),(1-sqrt(1+4x^2))/(2x)).

%C Product by A007318 is A104505.

%F Number triangle T(n,k)=C(n,(n+k)/2)(-1)^((n+k)/2)(1+(-1)^(n+k))/2.

%F abs(T(n,k)) = A108044(n,k).

%e Triangle begins

%e .1,

%e .0, -1,

%e .-2, 0, 1,

%e .0, 3, 0, -1,

%e .6, 0, -4, 0, 1,

%e .0, -10, 0, 5, 0, -1,

%e .-20, 0, 15, 0, -6, 0, 1,

%e .0, 35, 0, -21, 0, 7, 0, -1,

%e .70, 0, -56, 0, 28, 0, -8, 0, 1,

%e .0, -126, 0, 84, 0, -36, 0, 9, 0, -1,

%e .-252, 0, 210, 0, -120, 0, 45, 0, -10, 0, 1

%K easy,sign,tabl

%O 0,4

%A _Paul Barry_, Jun 17 2006