A124394 - OEIS

%I #2 Mar 30 2012 18:59:18

%S 1,0,1,-1,0,1,-2,-2,0,1,-3,-4,-3,0,1,-4,-5,-6,-4,0,1,-5,-4,-6,-8,-5,0,

%T 1,-6,0,0,-6,-10,-6,0,1,-7,8,14,8,-5,-12,-7,0,1,-8,21,36,36,20,-3,-14,

%U -8,0,1,-9,40,63,72,65,36,0,-16,-9,0,1

%N Inverse of Fine number renewal array.

%C Inverse of A065600. Row sums are A057681(n+1). Diagonal sums are A124395.

%F Riordan array ((1-2x)/(1-x)^2,x(1-2x)/(1-x)^2); Number triangle T(n,k)=sum{j=0..k+1, C(k+1,j)C(n-j+k+1,2k+1)(-2)^j};

%e Triangle begins

%e 1,

%e 0, 1,

%e -1, 0, 1,

%e -2, -2, 0, 1,

%e -3, -4, -3, 0, 1,

%e -4, -5, -6, -4, 0, 1,

%e -5, -4, -6, -8, -5, 0, 1,

%e -6, 0, 0, -6, -10, -6, 0, 1

%K easy,sign,tabl

%O 0,7

%A _Paul Barry_, Oct 30 2006