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 A384495 #8 May 31 2025 10:27:10
%S A384495 1,2,26,648,25094,1372100,99827020,9233563136,1045169591270,
%T A384495 140259346792380,21754963505429340,3823376222328582480,
%U A384495 749784319125445476092,162122841942093462239368,38288723630416561023861048,9801732906198391239249940800,2702731846233390353066363949830
%N A384495 a(n) = Sum_{k=0..n} binomial(n,k)^2 * abs(Stirling1(2*k,k)) * abs(Stirling1(2*n-2*k,n-k)).
%F A384495 a(n) ~ 2^(4*n - 1/2) * n^(n - 3/2) * w^(2*n) / ((w-1) * Pi^(3/2) * exp(n) * (2*w-1)^n), where w = -LambertW(-1, -exp(-1/2)/2) = 1.7564312086261696769827376166...
%t A384495 Table[Sum[Binomial[n,k]^2 * Abs[StirlingS1[2*k,k]] * Abs[StirlingS1[2*n-2*k, n-k]], {k, 0, n}], {n, 0, 20}]
%Y A384495 Cf. A187656, A187658, A384496, A384471.
%K A384495 nonn
%O A384495 0,2
%A A384495 _Vaclav Kotesovec_, May 31 2025