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%I #18 May 09 2019 08:03:29
%S 1,0,1,1,2,1,2,1,2,0,0,-3,-3,-8,-10,-16,-20,-29,-35,-47,-56,-72,-85,
%T -105,-122,-148,-171,-202,-231,-270,-306,-353,-397,-453,-507,-573,
%U -637,-715,-791,-881,-970,-1075,-1178,-1298,-1417,-1554,-1691,-1846,-2001,-2177,-2353,-2550,-2748,-2969
%N Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 5.
%C Difference of the number of partitions of n+4 into 4 parts and the number of partitions of n+4 into 5 parts. - _Wesley Ivan Hurt_, Apr 16 2019
%H Colin Barker, <a href="/A060024/b060024.txt">Table of n, a(n) for n = 0..1000</a>
%H P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s1-17.1.139">Perpetual reciprocants</a>, Proc. London Math. Soc., 17 (1886), 139-151; Coll. Papers II, pp. 584-596.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-1,-1,-1,1,1,1,0,0,-1,-1,1).
%F a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=1, a(6)=2, a(7)=1, a(8)=2, a(9)=0, a(10)=0, a(11)=-3, a(12)=-3, a(13)=-8, a(14)=-10, a(n) = a(n-1)+ a(n-2)-a(n-5)-a(n-6)-a(n-7)+a(n-8)+a(n-9)+a(n-10)-a(n-13)- a(n-14)+ a(n-15). - _Harvey P. Dale_, Dec 21 2015
%F a(n) = A026810(n+4) - A026811(n+4). - _Wesley Ivan Hurt_, Apr 16 2019
%F G.f.: (1 - x + x^2)*(1 - x^2 - x^3) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Apr 17 2019
%t CoefficientList[Series[(1-x-x^5)/(Times@@(1-x^Range[5])),{x,0,60}],x] (* or *) LinearRecurrence[{1,1,0,0,-1,-1,-1,1,1,1,0,0,-1,-1,1},{1,0,1,1,2,1,2,1,2,0,0,-3,-3,-8,-10},60] (* _Harvey P. Dale_, Dec 21 2015 *)
%o (PARI) Vec((1 - x + x^2)*(1 - x^2 - x^3) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40)) \\ _Colin Barker_, Apr 17 2019
%Y Cf. A026810, A026811.
%Y Cf. For other values of N: A060022 (N=3), A060023 (N=4), this sequence (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), A060028 (N=9), A060029 (N=10).
%K sign,easy
%O 0,5
%A _N. J. A. Sloane_, Mar 17 2001
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