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 A344130 #10 May 10 2021 06:23:59
%S A344130 1,2,7,32,131,562,2383,10124,42916,181844,769246,3250388,13716377,
%T A344130 57812466,243382957,1023463628,4299199426,18040918456,75632083258,
%U A344130 316774424568,1325591467994,5542462776932,23155074355078,96661979245880,403223735948096,1680858909265768
%N A344130 Expansion of Product_{k>=1} (1 + x^k)^binomial(2*k,k).
%F A344130 a(n) ~ 2^(2*n - 1/3) * exp(3*n^(1/3)/2^(2/3) - 1 + c) / (sqrt(3*Pi) * n^(5/6)), where c = Sum_{k>=2} (-1)^k * (1 - 1/sqrt(1 - 4^(1-k)))/k = -0.0680700790487788003241709878640131435678833005035785286095068...
%t A344130 nmax = 25; CoefficientList[Series[Product[(1 + x^k)^Binomial[2 k, k], {k, 1, nmax}], {x, 0, nmax}], x]
%t A344130 nmax = 25; CoefficientList[Series[Exp[Sum[-(-1)^j * (1/Sqrt[1 - 4*x^j] - 1)/j, {j, 1, nmax}]], {x, 0, nmax}], x]
%Y A344130 Cf. A000984, A304787, A344108.
%K A344130 nonn
%O A344130 0,2
%A A344130 _Vaclav Kotesovec_, May 10 2021