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 A346224 #36 Mar 06 2022 08:34:41
%S A346224 1,1,3,15,114,1170,15570,256410,5103000,119773080,3264445800,
%T A346224 101784097800,3591396824400,141958074258000,6236035482877200,
%U A346224 302218901402418000,16060366291617648000,930654556409161584000,58524794739862410960000,3976525824684785163792000
%N A346224 a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} 1 / ((n-2*k)! * 4^k * k!).
%F A346224 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( x + x^2 / 4 ).
%F A346224 a(n) = n! * Sum_{k=0..n} Stirling1(n,k) * Bell(k) / 2^(n-k).
%F A346224 D-finite with recurrence a(0) = a(1) = 1; a(n) = n * a(n-1) + n * (n-1)^2 * a(n-2) / 2.
%F A346224 a(n) ~ sqrt(Pi) * n^((3*n + 1)/2) / (2^(n/2) * exp((3*n + 1)/2 - sqrt(2*n))). - _Vaclav Kotesovec_, Jul 17 2021
%t A346224 Table[(n!)^2 Sum[1/((n - 2 k)! 4^k k!), {k, 0, Floor[n/2]}], {n, 0, 19}]
%t A346224 nmax = 19; CoefficientList[Series[Exp[x + x^2/4], {x, 0, nmax}], x] Range[0, nmax]!^2
%o A346224 (PARI) a(n) = (n!)^2 * sum(k=0, n\2, 1/((n-2*k)!*4^k*k!)); \\ _Michel Marcus_, Jul 17 2021
%Y A346224 Cf. A000085, A000898, A023998, A080599, A239840.
%K A346224 nonn,easy
%O A346224 0,3
%A A346224 _Ilya Gutkovskiy_, Jul 16 2021