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A152571 Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 4^(n - 1), T(n,k) = -4^(n - k - 1), 1 <= k <= n - 1.

%I A152571 #11 Jan 10 2019 02:20:14
%S A152571 -1,1,-1,4,-1,-1,16,-4,-1,-1,64,-16,-4,-1,-1,256,-64,-16,-4,-1,-1,
%T A152571 1024,-256,-64,-16,-4,-1,-1,4096,-1024,-256,-64,-16,-4,-1,-1,16384,
%U A152571 -4096,-1024,-256,-64,-16,-4,-1,-1,65536,-16384,-4096,-1024,-256,-64,-16,-4,-1,-1
%N A152571 Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 4^(n - 1), T(n,k) = -4^(n - k - 1), 1 <= k <= n - 1.
%F A152571 From _Franck Maminirina Ramaharo_, Jan 08 2019: (Start)
%F A152571 G.f.: -(1 - 5*y + 2*x*y^2)/(1 - (4 + x)*y + 4*x*y^2).
%F A152571 E.g.f.: -(4 - x - (2 - x)*exp(4*y) + (6 - 2*x)*exp(x*y))/(8 - 2*x). (End)
%e A152571 Triangle begins:
%e A152571       -1;
%e A152571        1,     -1;
%e A152571        4,     -1,     -1;
%e A152571       16,     -4,     -1,    -1;
%e A152571       64,    -16,     -4,    -1,    -1;
%e A152571      256,    -64,    -16,    -4,    -1,   -1;
%e A152571     1024,   -256,    -64,   -16,    -4,   -1,  -1;
%e A152571     4096,  -1024,   -256,   -64,   -16,   -4,  -1,  -1;
%e A152571    16384,  -4096,  -1024,  -256,   -64,  -16,  -4,  -1, -1;
%e A152571    65536, -16384,  -4096, -1024,  -256,  -64, -16,  -4, -1, -1;
%e A152571   262144, -65536, -16384, -4096, -1024, -256, -64, -16, -4, -1, -1;
%e A152571      ...
%t A152571 b[0] = {-1}; b[1] = {1, -1};
%t A152571 b[n_] := b[n] = Join[{4^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];
%t A152571 Flatten[Table[b[n], {n, 0, 10}]]
%o A152571 (Maxima)
%o A152571 T(n, k) := if k = n then -1 else if k = 0 then 4^(n - 1) else -4^(n - k - 1)$
%o A152571 create_list(T(n, k), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Jan 08 2019 */
%Y A152571 Row sums (except row 0): A020988.
%Y A152571 Cf. A057728, A152568, A152570, A152572.
%K A152571 sign,easy,tabl
%O A152571 0,4
%A A152571 _Roger L. Bagula_, Dec 08 2008
%E A152571 Edited by _Franck Maminirina Ramaharo_, Jan 08 2019