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 A361758 #4 Mar 23 2023 16:53:27 %S A361758 1,2,4,10,30,90,264,754,2106,5778,15628,41786,110678,290858,759312, %T A361758 1971042,5091442,13095586,33555988,85695978,218198158,554081146, %U A361758 1403588376,3547702610,8949110954,22532603954,56637795100,142141826074,356212187334,891481312842 %N A361758 a(n) = [x^n] (x^5 + 5*x^4 + 4*x^3 - 3*x + 1)/((1 - x)*(x^2 + 2*x - 1)^2). %F A361758 a(n) = ((3*n^2 - 7*n + 2)*a(n - 1) - (n^2 - n)*a(n - 3) - (n^2 - 3*n)*a(n - 2)) / ((n - 1)*(n - 2)) for n >= 4. %p A361758 a := proc(n) option remember; if n < 4 then return [1, 2, 4, 10][n + 1] fi; %p A361758 ((3*n^2 - 7*n + 2)*a(n - 1) - (n^2 - n)*a(n - 3) - (n^2 - 3*n)*a(n - 2))/((n - 1)*(n - 2)) end: seq(a(n), n = 0..29); %p A361758 # Alternative: %p A361758 ogf := (x^5 + 5*x^4 + 4*x^3 - 3*x + 1)/((1 - x)*(x^2 + 2*x - 1)^2): %p A361758 ser := series(ogf, x, 40): seq(coeff(ser, x, n), n = 0..29); %Y A361758 Cf. A361745. %K A361758 nonn %O A361758 0,2 %A A361758 _Peter Luschny_, Mar 23 2023