|
%I #19 Mar 14 2023 17:11:52
%S 1,-5,11,-14,12,-9,9,-13,20,-26,27,-25,26,-33,43,-49,47,-42,43,-53,67,
%T -77,78,-73,72,-82,98,-108,107,-102,104,-118,138,-151,150,-142,141,
%U -155,178,-194,194,-187,189,-206,230,-246,245,-235,235,-255,285,-305,305,-295,295,-315,345,-365,365
%N Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=6.
%H Colin Barker, <a href="/A275640/b275640.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_15">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-14,-29,-49,-71,-90,-101,-101,-90,-71,-49,-29,-14,-5,-1).
%F Equivalent g.f.: 1 / ((1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2)^2*(1+x+x^2+x^3+x^4)). - _Colin Barker_, Aug 10 2016
%t CoefficientList[Series[1/((1+x)^3(1-x+x^2)(1+x^2)(1+x+x^2)^2(1+ x+x^2+ x^3+x^4)),{x,0,100}],x] (* or *) LinearRecurrence[{-5,-14,-29,-49,-71,-90,-101,-101,-90,-71,-49,-29,-14,-5,-1},{1,-5,11,-14,12,-9,9,-13,20,-26,27,-25,26,-33,43},100] (* _Harvey P. Dale_, Mar 14 2023 *)
%Y Cf. A275638.
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Aug 09 2016
|
