# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a158472 Showing 1-1 of 1 %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, Rows n = 0..98, flattened %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE