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 A354843 #16 Jun 10 2022 11:08:07
%S A354843 1,5,19,145,601,8521,35281,672001,4898881,82615681,439084801,
%T A354843 21138606721,80951270401,3358578263041,49506372115201,
%U A354843 1227603183206401,6046686277632001,611515751899852801,2311256907767808001,254421414038266675201,4015778465971464192001
%N A354843 a(n) = n! * Sum_{d|n} (n/d)^d / d!.
%H A354843 Seiichi Manyama, <a href="/A354843/b354843.txt">Table of n, a(n) for n = 1..447</a>
%F A354843 E.g.f.: Sum_{k>0} (exp(k * x^k) - 1).
%F A354843 If p is prime, a(p) = 1 + p * p!.
%t A354843 a[n_] := n! * DivisorSum[n, (n/#)^#/#! &]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2022 *)
%o A354843 (PARI) a(n) = n!*sumdiv(n, d, (n/d)^d/d!);
%o A354843 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, exp(k*x^k)-1)))
%Y A354843 Cf. A057625, A327579, A354845.
%K A354843 nonn
%O A354843 1,2
%A A354843 _Seiichi Manyama_, Jun 08 2022