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 A318248 #20 Jul 16 2020 02:35:11
%S A318248 1,1,1,3,5,10,18,35,63,123,220,411,750,1387,2498,4649,8308,15150,
%T A318248 27446,49638,88754,161280,287831,516770,924956,1655166,2944850,
%U A318248 5272056,9348047,16631195,29569572,52421323,92665614,164437988,290243745,512649342,904774082
%N A318248 Expansion of Product_{k>=1} (1 + Fibonacci(k)*x^k).
%H A318248 Vaclav Kotesovec, <a href="/A318248/b318248.txt">Table of n, a(n) for n = 0..4500</a>
%H A318248 Michael Hendriksen, Nils Kapust, <a href="https://arxiv.org/abs/2004.00062">On the comparison of incompatibility of split systems across different taxa sizes</a>, arXiv:2004.00062 [q-bio.PE], 2020.
%F A318248 From _Vaclav Kotesovec_, Aug 24 2018: (Start)
%F A318248 a(n) ~ c * A000045(n) * exp(r*sqrt(n)) / n^(3/4) ~ c * exp(r*sqrt(n)) * phi^n / (sqrt(5) * n^(3/4)), where r = 2*sqrt(-polylog(2, -1/sqrt(5))) = 1.273105657580344020952907652385896290122122879833..., c = 0.4521555113342405268628694407039776... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
%F A318248 Equivalently, r = 2*sqrt(Pi^2/6 + log(5)^2/8 + polylog(2, -sqrt(5))). (End)
%t A318248 nmax = 50; CoefficientList[Series[Product[1 + Fibonacci[k]*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t A318248 nmax = 50; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[Do[poly[[j + 1]] += Fibonacci[k]*poly[[j - k + 1]], {j, nmax, k, -1}];, {k, 2, nmax}]; poly
%Y A318248 Cf. A000045, A022629, A300520, A318263, A318264.
%K A318248 nonn
%O A318248 0,4
%A A318248 _Vaclav Kotesovec_, Aug 22 2018