%I #3 Mar 30 2012 18:59:08
%S 1,1,1,-1,1,1,2,-2,2,1,-5,5,-4,5,1,13,-14,11,-7,12,1,-33,40,-35,20,-5,
%T 27,1,80,-111,113,-77,21,34,58,1,-184,293,-350,294,-144,-27,238,121,1,
%U 402,-731,1021,-1042,716,-249,-153,1063,248,1,-840,1726,-2796,3409,-2982,1755,-724,318,4037,503,1
%N Inverse binomial transform of number-theoretic triangle A109974.
%C First column is expansion of bracket function A001659.
%F T(n, k)=sum{j=1..n, (-1)^(n-j)C(n-1, j-1)*if(k<=j, sigma(k-1, j-k+1), 0)} [offset (1, 1)]
%e Rows begin
%e 1;
%e 1,1;
%e -1,1,1;
%e 2,-2,2,1;
%e -5,5,-4,5,1;
%e 13,-14,11,-7,12,1;
%e -33,40,-35,20,-5,27,1;
%K easy,sign,tabl
%O 1,7
%A _Paul Barry_, Jul 06 2005