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 A193005 #18 Jan 02 2021 04:21:29 %S A193005 0,1,2,11,40,115,280,611,1234,2357,4320,7677,13328,22733,38258,63735, %T A193005 105368,173199,283480,462511,752850,1223361,1985472,3219481,5217120, %U A193005 8450425,13683170,22151171,35854024,58027147,93905560,151959707,245895058,397887533 %N A193005 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. %C A193005 The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+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 A193005 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,6,1,-3,1). %F A193005 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 A193005 G.f.: -x*(1-3*x+10*x^2-3*x^3+x^4) / ( (x^2+x-1)*(x-1)^4 ). - _R. J. Mathar_, May 12 2014 %F A193005 a(n) = 10*F(n+4) + 4*F(n+5) - 50 - 24*n - 6*n^2 - n^3, where F = A000045. - _Greg Dresden_, Jan 01 2021 %t A193005 (See A193004.) %Y A193005 Cf. A192232, A192744, A192951, A193004, A000045. %K A193005 nonn %O A193005 0,3 %A A193005 _Clark Kimberling_, Jul 14 2011