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A160182 Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix.

%I A160182 #14 Mar 05 2019 02:17:45
%S A160182 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 A160182 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 A160182 Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix.
%C A160182 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 A160182 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 A160182 First few rows of the triangle:
%e A160182    1;
%e A160182    1,  1;
%e A160182    2,  1,  1;
%e A160182    3,  1,  1,  1;
%e A160182    5,  2,  1,  1,  1;
%e A160182    6,  2,  1,  1,  1,  1;
%e A160182   10,  4,  2,  1,  1,  1,  1;
%e A160182   11,  4,  2,  1,  1,  1,  1,  1;
%e A160182   16,  6,  3,  2,  1,  1,  1,  1,  1;
%e A160182   19,  7,  4,  2,  1,  1,  1,  1,  1,  1;
%e A160182   26, 10,  5,  3,  2,  1,  1,  1,  1,  1,  1;
%e A160182   ...
%p A160182 A160182den := proc(n,k)
%p A160182     a := add( A129184(n,i)*A051731(i,k),i=1..n) ;
%p A160182     if n =k then
%p A160182         -a+1 ;
%p A160182     else
%p A160182         -a;
%p A160182     end if;
%p A160182 end proc:
%p A160182 N := 20 :
%p A160182 M := Matrix(N,N) :
%p A160182 for n from 1 to N do
%p A160182 for k from 1 to N do
%p A160182     M[n,k] := A160182den(n,k) ;
%p A160182 end do:
%p A160182 end do:
%p A160182 MatrixInverse(M) ;  # _R. J. Mathar_, Aug 04 2015
%Y A160182 Cf. A051731, A129184, A160183.
%Y A160182 Row sums = A068336. Left border = A003238.
%K A160182 nonn,tabl
%O A160182 1,4
%A A160182 _Gary W. Adamson_, May 03 2009