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Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 10.
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%I #18 Oct 01 2023 13:08:26

%S 1,0,1,1,2,2,4,4,7,8,11,12,18,19,26,29,37,40,51,53,65,68,79,80,92,87,

%T 94,84,82,58,45,-1,-36,-109,-180,-297,-413,-594,-780,-1042,-1325,

%U -1704,-2112,-2647,-3228,-3961,-4772,-5769,-6867,-8206,-9682,-11446,-13402,-15710

%N Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 10.

%C Difference of the number of partitions of n+9 into 9 parts and the number of partitions of n+9 into 10 parts. - _Wesley Ivan Hurt_, Apr 16 2019

%H Ray Chandler, <a href="/A060029/b060029.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_55">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 1, 1, 1, 2, 0, 0, -1, -1, -1, -1, -3, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, -3, -1, -1, -1, -1, 0, 0, 2, 1, 1, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, 1, -1).

%F a(n) = A026815(n+9) - A026816(n+9). - _Wesley Ivan Hurt_, Apr 16 2019

%t CoefficientList[Series[(1-x-x^10)/Times@@(1-x^Range[10]),{x,0,60}],x] (* _Harvey P. Dale_, May 15 2016 *)

%Y Cf. A026815, A026816.

%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), A060028 (N=9), this sequence (N=10).

%K sign,easy

%O 0,5

%A _N. J. A. Sloane_, Mar 17 2001