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 A231291 #9 Oct 31 2014 06:19:11
%S A231291 1,1,3,9,29,99,355,1333,5213,21163,88899,385413,1720637,7894827,
%T A231291 37166563,179254501,884548253,4460597131,22962705027,120557527941,
%U A231291 644952640253,3512995320939,19468234666531,109694091843109,628027149163613,3651429293510731,21547912967252163
%N A231291 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1 + k*x) / (1 - x - k*x^2).
%C A231291 Compare to the identity:
%C A231291 Sum_{n>=0} x^n * Product_{k=1..n} (1 + k*x)/(1 + x + k*x^2) = 1/(1-x).
%H A231291 Vaclav Kotesovec, <a href="/A231291/b231291.txt">Table of n, a(n) for n = 0..300</a>
%e A231291 G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 29*x^4 + 99*x^5 + 355*x^6 + 1333*x^7 +...
%e A231291 where
%e A231291 A(x) = 1 + x*(1+x)/(1-x-x^2) + x^2*(1+x)*(1+2*x)/((1-x-x^2)*(1-x-2*x^2)) + x^3*(1+x)*(1+2*x)*(1+3*x)/((1-x-x^2)*(1-x-2*x^2)*(1-x-3*x^2)) + x^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)/((1-x-x^2)*(1-x-2*x^2)*(1-x-3*x^2)*(1-x-4*x^2)) +...
%o A231291 (PARI) {a(n)=polcoeff( sum(m=0, n, x^m*prod(k=1, m, (1+k*x)/(1-x-k*x^2 +x*O(x^n))) ), n)}
%o A231291 for(n=0, 30, print1(a(n), ", "))
%Y A231291 Cf. A204064, A231274.
%K A231291 nonn
%O A231291 0,3
%A A231291 _Paul D. Hanna_, Nov 06 2013