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%I #14 Mar 05 2019 02:17:45
%S 1,1,1,2,1,1,3,1,1,1,5,2,1,1,1,6,2,1,1,1,1,10,4,2,1,1,1,1,11,4,2,1,1,
%T 1,1,1,16,6,3,2,1,1,1,1,1,19,7,4,2,1,1,1,1,1,1,26,10,5,3,2,1,1,1,1,1,1
%N Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix.
%C Inverse mobius transform (A051731) * the triangle shifts row terms to the right deleting the right border, getting triangle A160183: (1; 2,1; 3,1,1; 5,2,1,1;...).
%F Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. The operations shift the inverse Mobius transform (A051731) down, changing the signs to (-1), then add I = (1,1,1,...) as the right border.
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 2, 1, 1;
%e 3, 1, 1, 1;
%e 5, 2, 1, 1, 1;
%e 6, 2, 1, 1, 1, 1;
%e 10, 4, 2, 1, 1, 1, 1;
%e 11, 4, 2, 1, 1, 1, 1, 1;
%e 16, 6, 3, 2, 1, 1, 1, 1, 1;
%e 19, 7, 4, 2, 1, 1, 1, 1, 1, 1;
%e 26, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1;
%e ...
%p A160182den := proc(n,k)
%p a := add( A129184(n,i)*A051731(i,k),i=1..n) ;
%p if n =k then
%p -a+1 ;
%p else
%p -a;
%p end if;
%p end proc:
%p N := 20 :
%p M := Matrix(N,N) :
%p for n from 1 to N do
%p for k from 1 to N do
%p M[n,k] := A160182den(n,k) ;
%p end do:
%p end do:
%p MatrixInverse(M) ; # _R. J. Mathar_, Aug 04 2015
%Y Cf. A051731, A129184, A160183.
%Y Row sums = A068336. Left border = A003238.
%K nonn,tabl
%O 1,4
%A _Gary W. Adamson_, May 03 2009
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