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%I #19 Oct 01 2023 13:06:45
%S 1,0,1,1,2,2,4,4,7,7,10,11,16,16,22,23,29,29,36,34,41,37,40,32,32,14,
%T 6,-22,-44,-90,-130,-203,-270,-378,-487,-642,-803,-1027,-1260,-1568,
%U -1899,-2320,-2774,-3342,-3955,-4706,-5526,-6507,-7579,-8854,-10243,-11872,-13656
%N Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 9.
%C Difference of the number of partitions of n+8 into 8 parts and the number of partitions of n+8 into 9 parts. - _Wesley Ivan Hurt_, Apr 16 2019
%H Ray Chandler, <a href="/A060028/b060028.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_45">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 2, 1, 1, 1, 0, -1, -1, -1, -2, -1, -1, 1, 1, 2, 1, 1, 1, 0, -1, -1, -1, -2, 0, 1, 0, 0, 1, 0, 1, 0, 0, -1, -1, 1).
%F a(n) = A026814(n+8) - A026815(n+8). - _Wesley Ivan Hurt_, Apr 16 2019
%t With[{den=Times@@Table[(1-x^n),{n,9}]},CoefficientList[Series[(1-x-x^9)/ den,{x,0,60}],x]] (* _Harvey P. Dale_, May 22 2012 *)
%Y Cf. A026814, A026815.
%Y Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), this sequence (N=9), A060029 (N=10).
%K sign,easy
%O 0,5
%A _N. J. A. Sloane_, Mar 17 2001
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