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 A356280 #10 Aug 02 2022 07:52:21
%S A356280 1,3,12,50,211,894,3791,16068,68032,287675,1214761,5122428,21571028,
%T A356280 90718913,381050570,1598645263,6699355413,28044720813,117281866330,
%U A356280 489999068614,2045341248508,8530263939665,35547083083270,148015639243691,615870619714675,2560734764460360
%N A356280 a(n) = Sum_{k=0..n} binomial(2*n, n-k) * p(k), where p(k) is the partition function A000041.
%H A356280 Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, VI.26. Catalan sums, p.417.
%F A356280 a(n) ~ 2^(2*n - 1/2) * exp(3^(1/3) * Pi^(4/3) * n^(1/3) / 4) / (3*Pi*n)^(2/3).
%t A356280 Table[Sum[PartitionsP[k]*Binomial[2*n, n-k], {k, 0, n}], {n, 0, 30}]
%t A356280 nmax = 30; CoefficientList[Series[Sum[PartitionsP[k]*((1-2*x-Sqrt[1-4*x])/(2*x))^k / Sqrt[1-4*x], {k, 0, nmax}], {x, 0, nmax}], x]
%Y A356280 Cf. A000041, A032443, A218481, A286955, A356267, A356281.
%K A356280 nonn
%O A356280 0,2
%A A356280 _Vaclav Kotesovec_, Aug 01 2022