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 A333616 #6 Apr 13 2020 17:06:30
%S A333616 0,1,3,6,6,10,10,15,15,21,21,28,28,36,36,45,45,55,55,66,66,78,78,91,
%T A333616 91,105,105,120,120,136,136,153,153,171,171,190,190,210,210,231,231,
%U A333616 253,253,276,276,300,300,325,325,351,351,378,378,406,406,435,435,465,465
%N A333616 Expansion of x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2).
%C A333616 For n > 0, a(n) is the n-th row sum of the triangle A333416.
%H A333616 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A333616 O.g.f.: x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2).
%F A333616 E.g.f.: ((8 + 9*x + x^2)*cosh(x) + (15 + 7*x + x^2)*sinh(x) - 8*(1 + 2*x))/8.
%F A333616 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 2.
%F A333616 a(n) = A008805(n+1) for n > 2.
%t A333616 LinearRecurrence[{1,2,-2,-1,1},{0,1,3,6,6,10,10,15},59]
%o A333616 (PARI) my(x='x + O('x^59)); concat([0], Vec(serlaplace(((8 + 9*x + x^2)*cosh(x) + (15 + 7*x + x^2)*sinh(x) - 8*(1 + 2*x))/8)))
%o A333616 (Sage) (x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2)).series(x, 59).coefficients(x, sparse=False)
%Y A333616 Cf. A000217, A008805, A333416.
%K A333616 easy,nonn
%O A333616 0,3
%A A333616 _Stefano Spezia_, Mar 29 2020