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A168228 Coefficient triangle sequence of characteristic polynomials of a Fermat like matrix:M(n)=Pascal n-th matrix: F(n)=Inverse[Transpose[M(n)]].M(n).

%I A168228 #4 Jun 02 2025 02:11:48
%S A168228 1,1,-1,1,-1,1,1,1,-1,-1,1,1,0,1,1,1,-5,10,-10,5,-1,1,-5,-4,25,-4,-5,
%T A168228 1,1,15,64,50,-50,-64,-15,-1,1,15,65,66,30,66,65,15,1,1,-55,455,-671,
%U A168228 1410,-1410,671,-455,55,-1,1,-55,1815,-4730,11495,-7251,11495,-4730,1815,-55
%N A168228 Coefficient triangle sequence of characteristic polynomials of a Fermat like matrix:M(n)=Pascal n-th matrix: F(n)=Inverse[Transpose[M(n)]].M(n).
%C A168228 Row sums are:
%C A168228 {1, 0, 1, 0, 4, 0, 9, 0, 324, 0, 9801, 0,...}
%C A168228 Example Matrix F(3):
%C A168228 {{1, 1, 1},
%C A168228 {-1, -3, -2},
%C A168228 {1, 2, 1}}
%D A168228 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 172.
%e A168228 {1},
%e A168228 {1, -1},
%e A168228 {1, -1, 1},
%e A168228 {1, 1, -1, -1},
%e A168228 {1, 1, 0, 1, 1},
%e A168228 {1, -5, 10, -10, 5, -1},
%e A168228 {1, -5, -4, 25, -4, -5, 1},
%e A168228 {1, 15, 64, 50, -50, -64, -15, -1},
%e A168228 {1, 15, 65, 66, 30, 66, 65, 15, 1},
%e A168228 {1, -55, 455, -671, 1410, -1410, 671, -455, 55, -1},
%e A168228 {1, -55, 1815, -4730, 11495, -7251, 11495, -4730, 1815, -55, 1},
%e A168228 {1, 197, 4675, -33825, -54978, 99174, -99174, 54978, 33825, -4675, -197, -1}
%t A168228 Clear[T, M, F];
%t A168228 T[n_, m_] := If[n >= m, Binomial[n, m], 0];
%t A168228 M[n_] := Table[T[k, m], {k, 0, n}, {m, 0, n}];
%t A168228 F[n_] := Inverse[Transpose[M[n]]].M[n];
%t A168228 Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[F[n], x], x], {n, 0, 10}]];
%t A168228 Flatten[%]
%Y A168228 A045912
%K A168228 sign,uned
%O A168228 0,17
%A A168228 _Roger L. Bagula_, Nov 20 2009