cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A060029 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 A060029 #18 Oct 01 2023 13:08:26
%S A060029 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 A060029 94,84,82,58,45,-1,-36,-109,-180,-297,-413,-594,-780,-1042,-1325,
%U A060029 -1704,-2112,-2647,-3228,-3961,-4772,-5769,-6867,-8206,-9682,-11446,-13402,-15710
%N A060029 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 10.
%C A060029 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 A060029 Ray Chandler, <a href="/A060029/b060029.txt">Table of n, a(n) for n = 0..1000</a>
%H A060029 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 A060029 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A060029 <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 A060029 a(n) = A026815(n+9) - A026816(n+9). - _Wesley Ivan Hurt_, Apr 16 2019
%t A060029 CoefficientList[Series[(1-x-x^10)/Times@@(1-x^Range[10]),{x,0,60}],x] (* _Harvey P. Dale_, May 15 2016 *)
%Y A060029 Cf. A026815, A026816.
%Y A060029 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 A060029 sign,easy
%O A060029 0,5
%A A060029 _N. J. A. Sloane_, Mar 17 2001