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 A331345 #27 Jun 09 2020 07:24:07
%S A331345 1,3,37,1015,48601,3583811,376372333,53343571695,9808511445361,
%T A331345 2270198126932219,645790373135121061,221449391959470686375,
%U A331345 90084675298978081317961,42890688646618728144279987,23627228721958495690763944861,14910259060767841554203065990111
%N A331345 a(n) = (1/n^2) * Sum_{k>=1} k^n * (1 - 1/n)^(k - 1).
%H A331345 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A331345 a(n) = n! * [x^n] (exp(x) - 1) / (exp(x) - n * (exp(x) - 1)).
%F A331345 a(n) = Sum_{k=1..n} Stirling2(n,k) * (n - 1)^(k - 1) * k!.
%F A331345 a(n) ~ sqrt(2*Pi) * n^(2*n - 1/2) / exp(n + 1/2). - _Vaclav Kotesovec_, Jun 08 2020
%t A331345 Join[{1}, Table[1/n^2 Sum[k^n (1 - 1/n)^(k - 1), {k, 1, Infinity}], {n, 2, 16}]]
%t A331345 Table[n! SeriesCoefficient[(Exp[x] - 1)/(Exp[x] - n (Exp[x] - 1)), {x, 0, n}], {n, 1, 16}]
%Y A331345 Cf. A000670, A050351, A050352, A050353, A094420, A257565, A321189, A334240.
%K A331345 nonn
%O A331345 1,2
%A A331345 _Ilya Gutkovskiy_, Jun 08 2020