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A122509 Coefficient expansion of the root sum zero polynomial:p(x)=-21 - 2 x + x^3 as x/(1 - x^2(2 + 21 x)). 0
0, 1, 0, 2, 21, 4, 84, 449, 252, 2662, 9933, 10616, 75768, 229825, 374472, 2050778, 5575269, 11965468, 54216876, 141011585, 359708580, 1420577566, 3680660445, 10395035312, 37193449776, 98083939969, 292682641104, 977230325234 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This sequence comes from investigating cubic root sum zero polynomials with rules: 1) p[x_] = Expand[Product[(x - a[n]), {n, 1, 3}]]=0 2) Sum[a[n], {n, 1, 3}]=0 Setting: a[1] = -a[2] - a[3] Solving for negative a[2] as first expansion term : Solve[a2^2 + a2 a3 + a3^2 == 2, a2] a[3]=3 Gives this sequence.

LINKS

Table of n, a(n) for n=1..28.

FORMULA

Coefficient expansion of x/(1 - x^2(2 + 21 x))

MATHEMATICA

p[x_]=-21 - 2 x + x^3 q[x_] = ExpandAll[x^3*p[1/x]] Table[ SeriesCoefficient[Series[x/q[x], {x, 0, 30}], n], {n, 0, 30}]

CROSSREFS

Sequence in context: A303218 A162536 A100980 * A024230 A105666 A058261

Adjacent sequences:  A122506 A122507 A122508 * A122510 A122511 A122512

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Sep 15 2006

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)