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%I #2 Mar 30 2012 17:35:17
%S 0,1,2,0,3,1,-1,0,4,2,0,1,-2,-2,1,0,5,3,1,2,-1,-1,2,1,-3,-4,-1,-3,2,3,
%T -1,0,6,4,2,3,0,0,3,2,-2,-3,0,-2,3,4,0,1,-4,-6,-3,-6,0,0,-4,-4,3,6,2,
%U 6,-2,-4,1,0,7,5,3,4,1,1,4,3,-1,-2,1,-1,4,5,1,2,-3,-5,-2,-5,1,1,-3,-3,4,7,3,7,-1,-3,2,1,-5,-8,-5,-9,-2
%N Inverse binomial sum of compositions in standard order.
%C The standard order of compositions is given by A066099.
%C This is the final term of the inverse binomial transform of the composition.
%F For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k (-1)^{i-1} C(k-1,i-1) b(i).
%e Composition number 11 is 2,1,1; 1*2-2*1+1*1 = 1, so a(11) = 1.
%e The table starts:
%e 0
%e 1
%e 2 0
%e 3 1 -1 0
%Y Cf. A066099, A124754, A124755, A011782 (row lengths), A001477 (row sums).
%K easy,sign,tabf
%O 0,3
%A _Franklin T. Adams-Watters_, Nov 06 2006
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