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A141681 The matrix inverse of the triangle A141680.

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%I A141681 #11 Jun 05 2018 22:33:25
%S A141681 1,-4,1,-9,0,1,32,-12,0,1,-25,0,0,0,1,504,-45,-40,0,0,1,-49,0,0,0,0,0,
%T A141681 1,-4096,1568,0,-140,0,0,0,1,2187,0,-252,0,0,0,0,0,1,13400,-225,0,0,
%U A141681 -504,0,0,0,0,1,-121,0,0,0,0,0,0,0,0,0,1
%N A141681 The matrix inverse of the triangle A141680.
%C A141681 Row sums are 1, -3, -8, 21, -24, 420, -48, -2667, 1936, 12672, ...
%H A141681 G. C. Greubel, <a href="/A141681/b141681.txt">Rows n=1..100 of triangle, flattened</a>
%F A141681 Sum_{j=k..n} T(n,j) * A141680(j,k) = delta(n,k).
%e A141681 Triangle begins
%e A141681       1;
%e A141681      -4,    1;
%e A141681      -9,    0,    1;
%e A141681      32,  -12,    0,    1;
%e A141681     -25,    0,    0,    0,    1;
%e A141681     504,  -45,  -40,    0,    0,    1;
%e A141681     -49,    0,    0,    0,    0,    0,    1;
%e A141681   -4096, 1568,    0, -140,    0,    0,    0,    1;
%e A141681    2187,    0, -252,    0,    0,    0,    0,    0,    1;
%e A141681   13400, -225,    0,    0, -504,    0,    0,    0,    0,    1;
%t A141681 t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]*Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]; Table[Sum[t[n, m], {m, 1, n}], {n, 1, 10}]; M = Inverse[Table[Table[t[n, m], {m, 1, 10}], {n, 1, 10}]]; Table[Table[M[[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[%]
%Y A141681 Cf. A126988.
%K A141681 tabl,sign
%O A141681 1,2
%A A141681 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 07 2008