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 A336589 #7 Jul 29 2020 16:58:01
%S A336589 1,0,-3,-19,-75,574,25795,579963,9342529,21955076,-7954085799,
%T A336589 -535479422655,-25206613635203,-871888114433454,-7465407495946777,
%U A336589 2538884115164554199,344689220434285963905,31689538033223254172648,2273498459548301881979029
%N A336589 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * BesselI(0,2*sqrt(1 - exp(x))).
%F A336589 a(n) = n! * Sum_{k=0..n} (-1)^k * Stirling2(n+1,k+1) / k!.
%t A336589 nmax = 18; CoefficientList[Series[Exp[x] BesselI[0, 2 Sqrt[1 - Exp[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A336589 Table[n! Sum[(-1)^k StirlingS2[n + 1, k + 1]/k!, {k, 0, n}], {n, 0, 18}]
%o A336589 (PARI) a(n) = n! * sum(k=0, n, (-1)^k*stirling(n+1,k+1,2) / k!); \\ _Michel Marcus_, Jul 29 2020
%Y A336589 Cf. A001569, A009940, A293037, A336588.
%K A336589 sign
%O A336589 0,3
%A A336589 _Ilya Gutkovskiy_, Jul 26 2020