A small factors sequence

[Gerald McGarvey]

An observation about the sequence a(n):
If a difference 'triangle' is formed by repeatedly taking the differences
b(n+6) = a(n+6) - a(n)
c(n+12) = b(n+12) - b(n+6) etc.
then the 7th iteration of these differences are
279936, -279936, -559872, -279936, 279936, 559872, 279936, -279936
the 8th differences are zero, and the 6th iterations also have small factors,
but not all the terms in this 'triangle' have small factors. I don't know 
if this
can help at all to explain the small factors, and I'm not following how the
sequence comes from the formula (I don't have Maple).
A curiosity: no term before a(43) is divisible by 7, but a(43) through a(49)
are all divisible by 7.

Sincerely,
Gerald

At 07:57 PM 12/3/2005, Creighton Dement wrote:
>Dear Seqfans,
>
>I came across a sequence given in Maple by
>seriestolist(series((1-16*x+56*x^3-140*x^4+28*x^6-16*x^7+28*x^2+56*x^5+x^8)/(x^2-x+1)^8,
>x=0,50));
>
>1, -8, -72, -120, 330, 1584, 1716, -3432, -12870, -11440, 19448, 63648,
>50388, -77520, -232560, -170544, 245157, 692208, 480700, -657800,
>-1776060, -1184040, 1560780, 4071600, 2629575, -3365856, -8544096,
>-5379616, 6724520, 16695360, 10295472, -12620256, -30761874, -18643560,
>22481940, 53956656, 32224114, -38320568, -90759240, -53524680, 62891499,
>147258144, 85900584, -99884400, -231550200, -133784560, 154143080,
>354201120, 202927725, -231917400
>
>By chance, I noticed that each term of the above sequence (in the range
>given) has small factors.  Pardon me for asking a vague question, but
>does the above sequence illustrate anything of interest in particular?
>
>p.s. I have visitors at the moment and, unfortunately, won't be able to
>look at the above again in detail until next week (though I am quite
>fortunate to have visitors!)
>
>Sincerely,
>Creighton
>
>-It's a shame when the girl of your dreams would still rather be with
>someone else when you're actually in a dream.