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.

A069957 Expansion of 1/((1-x)^2*(1-x^2)^2*(1-x^3)*(1-x^4)^2*(1-x^5)).

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%I A069957 #16 Oct 01 2023 13:23:46
%S A069957 1,2,5,9,18,30,51,79,124,183,270,382,540,740,1010,1347,1789,2333,3028,
%T A069957 3873,4932,6205,7772,9637,11901,14571,17770,21512,25948,31098,37143,
%U A069957 44113,52226,61522,72258,84489,98519,114418,132540,152976,176139,202141
%N A069957 Expansion of 1/((1-x)^2*(1-x^2)^2*(1-x^3)*(1-x^4)^2*(1-x^5)).
%H A069957 Vincenzo Librandi, <a href="/A069957/b069957.txt">Table of n, a(n) for n = 0..1000</a>
%H A069957 G. E. Andrews, P. Paule and A. Riese, <a href="http://dx.doi.org/10.1006/aama.2001.0733">MacMahon's Partition Analysis VIII: Plane partition diamonds</a>, Advances Applied Math., 27 (2001), 231-242.
%H A069957 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -3, 1, -2, -1, 4, 2, 0, -2, -2, -2, 0, 2, 4, -1, -2, 1, -3, 1, 2, -1).
%F A069957 G.f.: (1-x^3)*(1-x^5)/( Product_{j=1..5} 1-x^j )^2. - _G. C. Greubel_, Aug 17 2022
%t A069957 CoefficientList[Series[1/((1 - x)^2 (1 - x^2)^2 (1 - x^3) (1 - x^4)^2 (1 - x^5)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Sep 05 2016 *)
%o A069957 (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x^3)*(1-x^5)/(&*[1-x^j: j in [1..5]])^2 )); // _G. C. Greubel_, Aug 17 2022
%o A069957 (Sage)
%o A069957 def A069957_list(prec):
%o A069957     P.<x> = PowerSeriesRing(ZZ, prec)
%o A069957     return P( (1-x^3)*(1-x^5)/(product(1-x^j for j in (1..5)))^2 ).list()
%o A069957 A069957_list(60) # _G. C. Greubel_, Aug 17 2022
%Y A069957 Cf. A069950.
%K A069957 nonn
%O A069957 0,2
%A A069957 _N. J. A. Sloane_, May 05 2002