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%I #17 Aug 03 2014 14:01:40
%S 1,1,1,1,3,1,1,7,12,1,1,15,50,264,1,1,31,180,1920,11970,1,1,63,602,
%T 11760,146160,1689600,1,1,127,1932,66024,1477980,34214400,603233280,1,
%U 1,255,6050,353304,13556970,568656000,20043279360,586244602944,1
%N Lower triangular matrix in the LU-decomposition of the Vandermonde determinants generated by Fibonacci numbers.
%C If the Vandermonde matrix V = [F(i+2)^j]_(i,j=0)^n has LU-decomposition, then this triangle is given by L.
%H Vincenzo Librandi, <a href="/A210574/b210574.txt">Rows n = 0..70, flattened</a>
%e The triangle begins:
%e 1
%e 1, 1
%e 1, 3, 1
%e 1, 7, 12, 1
%e 1, 15, 50, 264, 1
%e 1, 31, 180, 1920, 11970, 1
%e 1, 63, 602, 11760, 146160, 1689600, 1
%e 1, 127, 1932, 66024, 1477980, 34214400, 603233280, 1
%e 1, 255, 6050, 353304, 13556970, 568656000, 20043279360, 586244602944, 1
%t n = 10; f = Fibonacci[Range[2, n + 1]]; m = Outer[ Power, f, Range[0, n - 1]]; mi = Transpose[LUDecomposition[m][[1]]]; Flatten[Table[Append[Take[mi[[i]], i - 1], 1], {i, n}]] (* _T. D. Noe_, Mar 22 2012 *)
%Y Cf. A203311, A210341.
%K nonn,tabl
%O 0,5
%A _Emanuele Munarini_, Mar 22 2012
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