cp's OEIS Frontend

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

%I A275638 #17 Oct 06 2017 04:28:35
%S A275638 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 A275638 13,-15,16,-15,14,-15,17,-18,18,-18,18,-18,19,-21,22,-21,20,-21,23,
%U A275638 -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 A275638 Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=4.
%H A275638 Colin Barker, <a href="/A275638/b275638.txt">Table of n, a(n) for n = 0..1000</a>
%H A275638 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 A275638 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 A275638 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-5,-6,-5,-3,-1)
%F A275638 Equivalent g.f.: 1 / ((1+x)^2*(1+x^2)*(1+x+x^2)). - _Colin Barker_, Aug 10 2016
%F A275638 From _Ilya Gutkovskiy_, Aug 10 2016: (Start)
%F A275638 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 A275638 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 A275638 f1:=k->(1-q)^k/mul(1-q^i,i=1..k);
%p A275638 f2:=k->series(f1(k),q,75);
%p A275638 f3:=k->seriestolist(f2(k));
%p A275638 f3(4);
%o A275638 (PARI) Vec(1/((1+x)^2*(1+x^2)*(1+x+x^2)) + O(x^100)) \\ _Colin Barker_, Aug 11 2016
%Y A275638 Cf. A275639, A275640, A275641, A275642, A275643, A275644.
%K A275638 sign,easy
%O A275638 0,2
%A A275638 _N. J. A. Sloane_, Aug 09 2016