A158472 - OEIS

A158472

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

1, 1, -1, 1, -2, 1, 1, -4, 5, -2, 1, -7, 17, -17, 6, 1, -12, 52, -102, 91, -30, 1, -20, 148, -518, 907, -758, 240, 1, -33, 408, -2442, 7641, -12549, 10094, -3120, 1, -54, 1101, -11010, 58923, -173010, 273623, -215094, 65520

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OFFSET

0,5

COMMENTS

Row sums of the unsigned triangle = A082480: (1, 2, 4, 12, 48, 288, 2592, ...).

Right border starting with row 1 (unsigned) = A003266: (1, 1, 2, 6, 30, 240, ...).

LINKS

Alois P. Heinz, Rows n = 0..98, flattened

EXAMPLE

First few rows of the unsigned triangle:

1, 1;

1, 2, 1;

1, 4, 5, 2;

1, 7, 17, 17, 6;

1, 12, 52, 102, 91, 30;

1, 20, 148, 518, 907, 758, 240;

1, 33, 408, 2442, 7641, 12549, 10094, 3120;

1, 54, 1101, 11010, 58923, 173010, 273623, 215094, 65520;

...

Example: row 5 is x^5 - 12x^4 + 52x^3 - 102x^2 + 91x - 30

= (x-1)*(x-1)*(x-2)*(x-3)*(x-5).

MAPLE

p:= proc(n) option remember; expand(`if`(n=0, 1,

p(n-1)*(x-(<<0|1>, <1|1>>^n)[1, 2])))

end:

T:= (n, k)-> coeff(p(n), x, n-k):

seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Nov 06 2016

MATHEMATICA

Array[Reverse@ CoefficientList[Times @@ Array[(x - Fibonacci@ #) &, #], x] &, 9, 0] // Flatten (* Michael De Vlieger, Apr 21 2019 *)

PROG

(PARI) row(n) = Vec(prod(k=1, n, x-fibonacci(k)));

for (n=0, 10, print(row(n))); \\ Michel Marcus, Apr 22 2019

CROSSREFS

Cf. A000045, A082480, A003266.

Sequence in context: A332404 A308905 A158471 * A198895 A355635 A118686

Adjacent sequences: A158469 A158470 A158471 * A158473 A158474 A158475

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Mar 20 2009

EXTENSIONS

One term corrected by Alois P. Heinz, Nov 06 2016

STATUS

approved