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 A229045 #6 Oct 28 2014 16:18:05
%S A229045 1,1,8,120,3516,166328,11532458,1100805591,138367161579,
%T A229045 22150155031528,4399449078063293,1061636331152735214,
%U A229045 305921694251090263429,103759120501255220937827,40916086296549562038319264,18562249570081891918836678474,9599588267110033395243891612720
%N A229045 O.g.f.: Sum_{n>=0} x^n * Product_{k=1..n} (n*k + x) / (1 + n*k*x).
%C A229045 Compare to a g.f. of Fibonacci numbers (A000045):
%C A229045 Sum_{n>=0} x^n * Product_{k=1..n} (k + x)/(1 + k*x).
%H A229045 Vaclav Kotesovec, <a href="/A229045/b229045.txt">Table of n, a(n) for n = 0..230</a>
%F A229045 a(n) ~ sqrt(Pi) * n^(2*n+1/2) / (sqrt(1-log(2)) * exp(2*n) * (log(2))^(2*n+1)). - _Vaclav Kotesovec_, Oct 28 2014
%e A229045 G.f.: A(x) = 1 + x + 8*x^2 + 120*x^3 + 3516*x^4 + 166328*x^5 +...
%e A229045 where
%e A229045 A(x) = 1 + x*(1+x)/(1+x) + x^2*(2+x)*(4+x)/((1+2*x)*(1+4*x)) + x^3*(3+x)*(6+x)*(9+x)/((1+3*x)*(1+6*x)*(1+9*x)) + x^4*(4+x)*(8+x)*(12+x)*(16+x)/((1+4*x)*(1+8*x)*(1+12*x)*(1+16*x)) +...
%o A229045 (PARI) {a(n)=polcoeff(sum(m=0, n, x^m*prod(k=1, m, m*k+x+x*O(x^n))/prod(k=1, m, 1+m*k*x+x*O(x^n))), n)}
%o A229045 for(n=0, 20, print1(a(n), ", ") )
%Y A229045 Cf. A220181, A230682.
%K A229045 nonn
%O A229045 0,3
%A A229045 _Paul D. Hanna_, Nov 02 2013