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A328647 Irregular triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of (1+x)/(x^2-3x+1)). 2
1, 1, 4, -2, -1, 11, -12, 3, 1, 29, -44, 24, -4, -1, 76, -145, 110, -40, 5, 1, 199, -456, 435, -220, 60, -6, -1, 521, -1393, 1596, -1015, 385, -84, 7, 1, 1364, -4168, 5572, -4256, 2030, -616, 112, -8, -1, 3571, -12276, 18756, -16716, 9576, -3654, 924, -144 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The first 201 polynomials are irreducible. Column 1 of the array: A002879 (odd-indexed Lucas numbers).  Row sums: A000032 (Lucas numbers). Alternating row sums: essentially 5*A030191.

LINKS

Table of n, a(n) for n=0..51.

MAPLE

First eight rows:

     1,     1;

     4,    -2,   -1;

    11,   -12,    3,     1;

    29,   -44,   24,    -4,   -1;

    76,  -145,  110,   -40,    5,    1;

   199,  -456,  435,  -220,   60,   -6,  -1;

   521, -1393, 1596, -1015,  385,  -84,   7,  1;

  1364, -4168, 5572, -4256, 2030, -616, 112, -8, -1;

First eight polynomials:

1 + x

4 - 2 x - x^2

11 - 12 x + 3 x^2 + x^3

29 - 44 x + 24 x^2 - 4 x^3 - x^4

76 - 145 x + 110 x^2 - 40 x^3 + 5 x^4 + x^5

199 - 456 x + 435 x^2 - 220 x^3 + 60 x^4 - 6 x^5 - x^6

521 - 1393 x + 1596 x^2 - 1015 x^3 + 385 x^4 - 84 x^5 + 7 x^6 + x^7

1364 - 4168 x + 5572 x^2 - 4256 x^3 + 2030 x^4 - 616 x^5 + 112 x^6 - 8 x^7 - x^8

MATHEMATICA

g[x_, n_] := Numerator[ Factor[D[(1 + x)/(x^2 - 3 x + 1), {x, n}]]]

Column[Expand[Table[g[x, n]/n!, {n, 0, 12}]]] (* polynomials *)

h[n_] := CoefficientList[g[x, n]/n!, x]

Table[h[n], {n, 0, 10}]

Column[%]  (* A328647 array *)

CROSSREFS

Cf. A328646, A002879, A000032.

Sequence in context: A193607 A075397 A049429 * A183158 A174005 A152818

Adjacent sequences:  A328644 A328645 A328646 * A328648 A328649 A328650

KEYWORD

tabf,sign

AUTHOR

Clark Kimberling, Nov 01 2019

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)