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A109978 Inverse binomial transform of number-theoretic triangle A109974. 1

%I

%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

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Last modified August 10 11:12 EDT 2020. Contains 336379 sequences. (Running on oeis4.)