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 A193007 #15 Feb 18 2025 08:17:43
%S A193007 0,1,1,9,36,108,268,591,1201,2303,4232,7534,13096,22357,37649,62749,
%T A193007 103772,170616,279300,455747,741905,1205651,1956816,3173114,5142096,
%U A193007 8329033,13486753,21833361,35339796,57195108,92559292,149781399,242370481
%N A193007 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
%C A193007 The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)-1+n^3, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.
%H A193007 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,6,1,-3,1).
%F A193007 a(n) = 5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).
%F A193007 G.f.: -x*(2*x^4-6*x^3+13*x^2-4*x+1)/((x-1)^4*(x^2+x-1)). [_Colin Barker_, Nov 12 2012]
%t A193007 (See A193006.)
%t A193007 LinearRecurrence[{5,-9,6,1,-3,1},{0,1,1,9,36,108},40] (* _Harvey P. Dale_, Sep 13 2021 *)
%Y A193007 Cf. A192232, A192744, A192951, A193006.
%K A193007 nonn,easy
%O A193007 0,4
%A A193007 _Clark Kimberling_, Jul 14 2011