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 A243633 #6 Jun 08 2014 08:55:25 %S A243633 1,1,3,8,21,56,152,417,1149,3169,8738,24083,66356,182806,503597, %T A243633 1387317,3821839,10528644,29005093,79905508,220130016,606431481, %U A243633 1670644817,4602422317,12679110454,34929397819,96226217048,265091454958 %N A243633 Expansion of (4*x^3-6*x^2+4*x-1)/(5*x^3-8*x^2+5*x-1). %F A243633 a(n) = sum(m=0..n, sum(k=0..n/2, binomial(m+k-1,k)*binomial(n+m-1,n-4*k-m))). %F A243633 A(x) = 1/(1-F(x)), where F(x) is g.f. A038504. %o A243633 (Maxima) %o A243633 a(n):=sum(sum(binomial(m+k-1,k)*binomial(n+m-1,n-4*k-m),k,0,n/2),m,0,n); %Y A243633 cf. A038504 %K A243633 nonn %O A243633 0,3 %A A243633 _Vladimir Kruchinin_, Jun 08 2014