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.
%I A103505 #44 Jul 03 2023 07:53:55
%S A103505 1,1,2,6,12,20,30,42,56,72,90,110,132,156,182,210,240,272,306,342,380,
%T A103505 420,462,506,552,600,650,702,756,812,870,930,992,1056,1122,1190,1260,
%U A103505 1332,1406,1482,1560,1640,1722,1806,1892,1980,2070,2162,2256,2352,2450
%N A103505 Denominator in expansion of (1-x)*log(1-x).
%C A103505 Apart from initial terms, same as A002378.
%C A103505 See A002378 for many more comments and references.
%C A103505 Denominators for the sequence with o.g.f. (1-x)*log(1-x). Numerators are given by 1 - 0^n - 2(C(1,n) - C(0,n)). Also denominators for the sequence with o.g.f. (1+x)*log(1+x). This sequence has numerators (-1)^n - 0^n + 2(C(1,n) - C(0,n)).
%C A103505 Also the denominator of the least distance between two adjacent Farey fractions of order n. The numerator is 1. - _Robert G. Wilson v_, Apr 13 2014
%C A103505 For n>0, a(n) are the Engel expansion of A096789. - _Benedict W. J. Irwin_, Dec 15 2016
%C A103505 Number of permutations of length n>=0 avoiding the partially ordered pattern (POP) {1>2} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the second one. - _Sergey Kitaev_, Dec 08 2020
%H A103505 Michael De Vlieger, <a href="/A103505/b103505.txt">Table of n, a(n) for n = 0..10000</a>
%H A103505 Alice L. L. Gao and Sergey Kitaev, <a href="https://arxiv.org/abs/1903.08946">On partially ordered patterns of length 4 and 5 in permutations</a>, arXiv:1903.08946 [math.CO], 2019.
%H A103505 Alice L. L. Gao and Sergey Kitaev, <a href="https://doi.org/10.37236/8605">On partially ordered patterns of length 4 and 5 in permutations</a>, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
%H A103505 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F A103505 G.f.: (1-2*x+2*x^2+2*x^3-x^4) / (1-x)^3;
%F A103505 a(n) = 0^n + C(1, n) - C(0, n) + 2*C(n, 2).
%t A103505 CoefficientList[Series[(1-2x+2x^2+2x^3-x^4)/(1-x)^3,{x,0,50}],x] (* or *) Denominator/@CoefficientList[Normal[Series[(1-x)Log[1-x], {x,0,50}]], x] (* _Harvey P. Dale_, Apr 20 2011 *)
%o A103505 (Magma) [0^n+Binomial(1,n)-Binomial(0,n)+2*Binomial(n,2): n in [0..60]]; // _Vincenzo Librandi_, Dec 18 2016
%Y A103505 Cf. A000384.
%K A103505 easy,nonn,frac
%O A103505 0,3
%A A103505 _Paul Barry_, Feb 09 2005