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 A318263 #10 Aug 24 2018 11:03:20
%S A318263 1,1,3,7,11,30,62,129,235,541,1034,2101,4140,8129,15984,31903,60398,
%T A318263 117646,228808,433768,836552,1601282,3031299,5736396,10899112,
%U A318263 20466182,38556342,72522116,135662847,253047629,473785878,878655661,1634304062,3033385668,5608183925
%N A318263 Expansion of Product_{k>=1} (1 + Lucas(k)*x^k).
%H A318263 Vaclav Kotesovec, <a href="/A318263/b318263.txt">Table of n, a(n) for n = 0..4500</a>
%F A318263 From _Vaclav Kotesovec_, Aug 24 2018: (Start)
%F A318263 a(n) ~ c * A000032(n) * A000009(n) ~ c * phi^n * exp(Pi*sqrt(n/3)) / (4 * 3^(1/4) * n^(3/4)), where c = Product_{k>=1} ((1 + Lucas(k)/phi^k)/2) = 0.8503149035690839100210269103058319341315494385103929947491... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
%F A318263 Equivalently, c = Product_{k>=1} (1 + (-1)^k/(2*phi^(2*k))),
%F A318263 c = 2/3 * QPochhammer[-1/2, -1/GoldenRatio^2]. (End)
%t A318263 nmax = 40; CoefficientList[Series[Product[1+LucasL[k]*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t A318263 nmax = 40; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[Do[poly[[j + 1]] += LucasL[k]*poly[[j - k + 1]], {j, nmax, k, -1}];, {k, 2, nmax}]; poly
%Y A318263 Cf. A000032, A022629, A318248, A318264.
%K A318263 nonn
%O A318263 0,3
%A A318263 _Vaclav Kotesovec_, Aug 22 2018