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A275638 Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=4. 8

%I

%S 1,-3,4,-3,2,-3,5,-6,6,-6,6,-6,7,-9,10,-9,8,-9,11,-12,12,-12,12,-12,

%T 13,-15,16,-15,14,-15,17,-18,18,-18,18,-18,19,-21,22,-21,20,-21,23,

%U -24,24,-24,24,-24,25,-27,28,-27,26,-27,29,-30,30,-30,30,-30,31,-33,34,-33,32,-33,35,-36,36

%N Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=4.

%H Colin Barker, <a href="/A275638/b275638.txt">Table of n, a(n) for n = 0..1000</a>

%H A. M. Odlyzko, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa49/aa4932.pdf">Differences of the partition function</a>, Acta Arithmetica 49.3 (1988): 237-254.

%H Dennis Stanton and Doron Zeilberger, <a href="https://doi.org/10.1090/S0002-9939-1989-0972238-1">The Odlyzko conjecture and O’Hara’s unimodality proof</a>, Proceedings of the American Mathematical Society 107.1 (1989): 39-42.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-5,-6,-5,-3,-1)

%F Equivalent g.f.: 1 / ((1+x)^2*(1+x^2)*(1+x+x^2)). - _Colin Barker_, Aug 10 2016

%F From _Ilya Gutkovskiy_, Aug 10 2016: (Start)

%F a(n) = -3*a(n-1) - 5*a(n-2) - 6*a(n-3) - 5*a(n-4) - 3*a(n-5) - a(n-6).

%F a(n) = (sqrt(3)*(-1)^n*n + 3*sqrt(3)*(-1)^n - 4*sin(2*Pi n/3) - sqrt(3)*cos(Pi*n/2))/(2*sqrt(3)). (End)

%p f1:=k->(1-q)^k/mul(1-q^i,i=1..k);

%p f2:=k->series(f1(k),q,75);

%p f3:=k->seriestolist(f2(k));

%p f3(4);

%o (PARI) Vec(1/((1+x)^2*(1+x^2)*(1+x+x^2)) + O(x^100)) \\ _Colin Barker_, Aug 11 2016

%Y Cf. A275639, A275640, A275641, A275642, A275643, A275644.

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Aug 09 2016

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)