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 A354891 #19 Jun 11 2022 07:52:07
%S A354891 1,3,7,73,121,9721,5041,1760641,44452801,562615201,39916801,
%T A354891 3156125575681,6227020801,192873372531841,222245415808416001,
%U A354891 14806216643368550401,355687428096001,34884164976924636172801,121645100408832001
%N A354891 a(n) = n! * Sum_{d|n} d^(n - d) / d!.
%H A354891 Seiichi Manyama, <a href="/A354891/b354891.txt">Table of n, a(n) for n = 1..305</a>
%F A354891 E.g.f.: Sum_{k>0} x^k/(k! * (1 - (k * x)^k)).
%F A354891 If p is prime, a(p) = 1 + p! = A038507(p).
%t A354891 a[n_] := n! * DivisorSum[n, #^(n - #)/#! &]; Array[a, 19] (* _Amiram Eldar_, Jun 10 2022 *)
%o A354891 (PARI) a(n) = n!*sumdiv(n, d, d^(n-d)/d!);
%o A354891 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-(k*x)^k)))))
%Y A354891 Cf. A038507, A342628, A354888, A354890, A354893.
%K A354891 nonn
%O A354891 1,2
%A A354891 _Seiichi Manyama_, Jun 10 2022