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%I #17 Oct 01 2023 13:04:48
%S 1,0,1,1,2,2,4,4,6,6,9,9,13,12,16,15,18,15,18,12,12,2,-3,-20,-31,-59,
%T -81,-122,-160,-222,-280,-369,-457,-581,-708,-878,-1055,-1286,-1528,
%U -1833,-2158,-2559,-2985,-3504,-4059,-4721,-5433,-6271,-7172,-8224,-9355,-10660,-12067
%N Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 8.
%C Difference of the number of partitions of n+7 into 7 parts and the number of partitions of n+7 into 8 parts. - _Wesley Ivan Hurt_, Apr 16 2019
%H Ray Chandler, <a href="/A060027/b060027.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_36">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 0, -1, 0, -1, 0, 1, 2, 1, 0, 1, -1, -1, -2, -1, -1, 1, 0, 1, 2, 1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, -1).
%F a(n) = A026813(n+7) - A026814(n+7). - _Wesley Ivan Hurt_, Apr 16 2019
%t With[{nn=8},CoefficientList[Series[(1-x-x^nn)/Times@@(1-x^Range[nn]),{x,0,60}],x]] (* _Harvey P. Dale_, May 15 2016 *)
%Y Cf. A026813, A026814.
%Y Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), this sequence (N=8), A060028 (N=9), A060029 (N=10).
%K sign,easy
%O 0,5
%A _N. J. A. Sloane_, Mar 17 2001