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A158472 Triangle read by rows: n-th row is the expansion of the polynomial (x-F1)*(x-F2)*(x-F3)*...*(x-Fn).

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