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 A336588 #9 Jul 28 2020 11:15:16
%S A336588 1,2,9,67,725,10616,200767,4740149,136113217,4656324934,186642121061,
%T A336588 8647446227487,457854954921949,27435354945248732,1844986431192663683,
%U A336588 138229607701444447561,11464234006789370705537,1046538415206891196153834,104623195637603009050593697
%N A336588 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * BesselI(0,2*sqrt(exp(x) - 1)).
%F A336588 a(n) = n! * Sum_{k=0..n} Stirling2(n+1,k+1) / k!.
%t A336588 nmax = 18; CoefficientList[Series[Exp[x] BesselI[0, 2 Sqrt[Exp[x] - 1]], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A336588 Table[n! Sum[StirlingS2[n + 1, k + 1]/k!, {k, 0, n}], {n, 0, 18}]
%o A336588 (PARI) a(n) = n! * sum(k=0, n, stirling(n+1,k+1,2) / k!); \\ _Michel Marcus_, Jul 27 2020
%Y A336588 Cf. A000110, A002720, A119392, A336589.
%K A336588 nonn
%O A336588 0,2
%A A336588 _Ilya Gutkovskiy_, Jul 26 2020