%I #16 Apr 22 2019 22:14:41
%S 1,1,-1,1,-2,1,1,-4,5,-2,1,-7,17,-17,6,1,-12,52,-102,91,-30,1,-20,148,
%T -518,907,-758,240,1,-33,408,-2442,7641,-12549,10094,-3120,1,-54,1101,
%U -11010,58923,-173010,273623,-215094,65520
%N Triangle read by rows: n-th row is the expansion of the polynomial (x-F1)*(x-F2)*(x-F3)*...*(x-Fn).
%C Row sums of the unsigned triangle = A082480: (1, 2, 4, 12, 48, 288, 2592, ...).
%C Right border starting with row 1 (unsigned) = A003266: (1, 1, 2, 6, 30, 240, ...).
%H Alois P. Heinz, <a href="/A158472/b158472.txt">Rows n = 0..98, flattened</a>
%e First few rows of the unsigned triangle:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 4, 5, 2;
%e 1, 7, 17, 17, 6;
%e 1, 12, 52, 102, 91, 30;
%e 1, 20, 148, 518, 907, 758, 240;
%e 1, 33, 408, 2442, 7641, 12549, 10094, 3120;
%e 1, 54, 1101, 11010, 58923, 173010, 273623, 215094, 65520;
%e ...
%e Example: row 5 is x^5 - 12x^4 + 52x^3 - 102x^2 + 91x - 30
%e = (x-1)*(x-1)*(x-2)*(x-3)*(x-5).
%p p:= proc(n) option remember; expand(`if`(n=0, 1,
%p p(n-1)*(x-(<<0|1>, <1|1>>^n)[1, 2])))
%p end:
%p T:= (n, k)-> coeff(p(n), x, n-k):
%p seq(seq(T(n, k), k=0..n), n=0..10); # _Alois P. Heinz_, Nov 06 2016
%t Array[Reverse@ CoefficientList[Times @@ Array[(x - Fibonacci@ #) &, #], x] &, 9, 0] // Flatten (* _Michael De Vlieger_, Apr 21 2019 *)
%o (PARI) row(n) = Vec(prod(k=1, n, x-fibonacci(k)));
%o for (n=0, 10, print(row(n))); \\ _Michel Marcus_, Apr 22 2019
%Y Cf. A000045, A082480, A003266.
%K tabl,sign
%O 0,5
%A _Gary W. Adamson_, Mar 20 2009
%E One term corrected by _Alois P. Heinz_, Nov 06 2016
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